Semantic Graph — Visual Examination Report

{
  "nodes": [
    {
      "id": "__equals_1",
      "type": "relation",
      "op": "equals",
      "subexpr": "F = m a",
      "chartScript": {
        "script": "F - a*m",
        "variables": [
          "F",
          "a",
          "m"
        ]
      }
    },
    {
      "id": "F",
      "type": "scalar",
      "latex": "F",
      "subexpr": "F",
      "chartScript": {
        "script": "F",
        "variables": [
          "F"
        ]
      }
    },
    {
      "id": "__multiply_2",
      "type": "operator",
      "op": "multiply",
      "subexpr": "m a",
      "chartScript": {
        "script": "a*m",
        "variables": [
          "a",
          "m"
        ]
      }
    },
    {
      "id": "m",
      "type": "scalar",
      "latex": "m",
      "subexpr": "m",
      "chartScript": {
        "script": "m",
        "variables": [
          "m"
        ]
      }
    },
    {
      "id": "a",
      "type": "scalar",
      "latex": "a",
      "subexpr": "a",
      "chartScript": {
        "script": "a",
        "variables": [
          "a"
        ]
      }
    }
  ],
  "edges": [
    {
      "from": "F",
      "to": "__equals_1"
    },
    {
      "from": "m",
      "to": "__multiply_2",
      "semantic": "direct",
      "weight": 1.0
    },
    {
      "from": "a",
      "to": "__multiply_2",
      "semantic": "direct",
      "weight": 1.0
    },
    {
      "from": "__multiply_2",
      "to": "__equals_1"
    }
  ],
  "classification": {
    "kind": "algebraic"
  }
}

flowchart RL
  classDef scalar fill:#1b3a1e,stroke:#66bb6a,color:#c8e6c9,font-size:15px
  classDef vector fill:#1b3a1e,stroke:#66bb6a,color:#c8e6c9,font-size:15px
  classDef constant fill:#1b3a1e,stroke:#66bb6a,color:#c8e6c9,font-size:15px
  classDef number fill:#1b3a1e,stroke:#66bb6a,color:#c8e6c9,font-size:15px
  classDef expression fill:#1b3a1e,stroke:#66bb6a,color:#c8e6c9,font-size:15px
  classDef text fill:#1b3a1e,stroke:#66bb6a,color:#c8e6c9,font-size:15px
  classDef operator fill:#1a2740,stroke:#42a5f5,color:#bbdefb,font-size:15px
  classDef function fill:#1a2740,stroke:#42a5f5,color:#bbdefb,font-size:15px
  classDef relation fill:#332a0b,stroke:#ffa726,color:#ffe0b2,font-size:15px
  classDef result fill:#332a0b,stroke:#ffa726,color:#ffe0b2,font-size:15px
  classDef annotation fill:#131a2c,stroke:#4a5580,color:#b0bcd0,font-size:15px
  __equals_1{"="}:::relation
  F["$F$"]:::scalar
  __multiply_2(("$\times$")):::operator
  m["$m$"]:::scalar
  a["$a$"]:::scalar
  F --> __equals_1
  m --> __multiply_2
  a --> __multiply_2
  __multiply_2 --> __equals_1
  linkStyle 0 stroke:#aaa,stroke-width:2px
  linkStyle 1 stroke:#ef5350,stroke-width:3px
  linkStyle 2 stroke:#ef5350,stroke-width:3px
  linkStyle 3 stroke:#aaa,stroke-width:2px

{
  "nodes": [
    {
      "id": "__equals_1",
      "type": "relation",
      "op": "equals",
      "subexpr": "W = m g",
      "chartScript": {
        "script": "W - g*m",
        "variables": [
          "W",
          "g",
          "m"
        ]
      }
    },
    {
      "id": "W",
      "type": "scalar",
      "latex": "W",
      "subexpr": "W",
      "chartScript": {
        "script": "W",
        "variables": [
          "W"
        ]
      }
    },
    {
      "id": "__multiply_2",
      "type": "operator",
      "op": "multiply",
      "subexpr": "m g",
      "chartScript": {
        "script": "g*m",
        "variables": [
          "g",
          "m"
        ]
      }
    },
    {
      "id": "m",
      "type": "scalar",
      "latex": "m",
      "subexpr": "m",
      "chartScript": {
        "script": "m",
        "variables": [
          "m"
        ]
      }
    },
    {
      "id": "g",
      "type": "scalar",
      "latex": "g",
      "subexpr": "g",
      "chartScript": {
        "script": "g",
        "variables": [
          "g"
        ]
      }
    }
  ],
  "edges": [
    {
      "from": "W",
      "to": "__equals_1"
    },
    {
      "from": "m",
      "to": "__multiply_2",
      "semantic": "direct",
      "weight": 1.0
    },
    {
      "from": "g",
      "to": "__multiply_2",
      "semantic": "direct",
      "weight": 1.0
    },
    {
      "from": "__multiply_2",
      "to": "__equals_1"
    }
  ],
  "classification": {
    "kind": "algebraic"
  }
}

flowchart RL
  classDef scalar fill:#1b3a1e,stroke:#66bb6a,color:#c8e6c9,font-size:15px
  classDef vector fill:#1b3a1e,stroke:#66bb6a,color:#c8e6c9,font-size:15px
  classDef constant fill:#1b3a1e,stroke:#66bb6a,color:#c8e6c9,font-size:15px
  classDef number fill:#1b3a1e,stroke:#66bb6a,color:#c8e6c9,font-size:15px
  classDef expression fill:#1b3a1e,stroke:#66bb6a,color:#c8e6c9,font-size:15px
  classDef text fill:#1b3a1e,stroke:#66bb6a,color:#c8e6c9,font-size:15px
  classDef operator fill:#1a2740,stroke:#42a5f5,color:#bbdefb,font-size:15px
  classDef function fill:#1a2740,stroke:#42a5f5,color:#bbdefb,font-size:15px
  classDef relation fill:#332a0b,stroke:#ffa726,color:#ffe0b2,font-size:15px
  classDef result fill:#332a0b,stroke:#ffa726,color:#ffe0b2,font-size:15px
  classDef annotation fill:#131a2c,stroke:#4a5580,color:#b0bcd0,font-size:15px
  __equals_1{"="}:::relation
  W["$W$"]:::scalar
  __multiply_2(("$\times$")):::operator
  m["$m$"]:::scalar
  g["$g$"]:::scalar
  W --> __equals_1
  m --> __multiply_2
  g --> __multiply_2
  __multiply_2 --> __equals_1
  linkStyle 0 stroke:#aaa,stroke-width:2px
  linkStyle 1 stroke:#ef5350,stroke-width:3px
  linkStyle 2 stroke:#ef5350,stroke-width:3px
  linkStyle 3 stroke:#aaa,stroke-width:2px

{
  "nodes": [
    {
      "id": "__equals_1",
      "type": "relation",
      "op": "equals",
      "subexpr": "E_k = \\frac{1}{2} m v^2",
      "chartScript": {
        "script": "E_k - 1/2*m*pow(v, 2)",
        "variables": [
          "E_k",
          "m",
          "v"
        ]
      }
    },
    {
      "id": "E_k",
      "type": "scalar",
      "latex": "E_{k}",
      "subexpr": "E_{k}",
      "chartScript": {
        "script": "E_k",
        "variables": [
          "E_k"
        ]
      }
    },
    {
      "id": "__multiply_2",
      "type": "operator",
      "op": "multiply",
      "subexpr": "\\frac{1}{2} m v^{2}",
      "chartScript": {
        "script": "(1/2)*m*pow(v, 2)",
        "variables": [
          "m",
          "v"
        ]
      }
    },
    {
      "id": "__power_3",
      "type": "operator",
      "latex": "\\dfrac{1}{(\\cdot)}",
      "op": "power",
      "exponent": "-1",
      "subexpr": "\\frac{1}{2}",
      "chartScript": {
        "script": "1/2",
        "variables": []
      }
    },
    {
      "id": "__num_4",
      "type": "number",
      "label": "2",
      "subexpr": "2",
      "chartScript": {
        "script": "2",
        "variables": []
      }
    },
    {
      "id": "__multiply_5",
      "type": "operator",
      "op": "multiply",
      "subexpr": "m v^{2}",
      "chartScript": {
        "script": "m*pow(v, 2)",
        "variables": [
          "m",
          "v"
        ]
      }
    },
    {
      "id": "m",
      "type": "scalar",
      "latex": "m",
      "subexpr": "m",
      "chartScript": {
        "script": "m",
        "variables": [
          "m"
        ]
      }
    },
    {
      "id": "__power_6",
      "type": "operator",
      "op": "power",
      "exponent": "2",
      "subexpr": "v^{2}",
      "chartScript": {
        "script": "pow(v, 2)",
        "variables": [
          "v"
        ]
      }
    },
    {
      "id": "v",
      "type": "scalar",
      "latex": "v",
      "subexpr": "v",
      "chartScript": {
        "script": "v",
        "variables": [
          "v"
        ]
      }
    }
  ],
  "edges": [
    {
      "from": "E_k",
      "to": "__equals_1"
    },
    {
      "from": "__num_4",
      "to": "__power_3"
    },
    {
      "from": "__power_3",
      "to": "__multiply_2"
    },
    {
      "from": "m",
      "to": "__multiply_5",
      "semantic": "direct",
      "weight": 1.0
    },
    {
      "from": "v",
      "to": "__power_6"
    },
    {
      "from": "__power_6",
      "to": "__multiply_5",
      "semantic": "direct",
      "weight": 1.0
    },
    {
      "from": "__multiply_5",
      "to": "__multiply_2",
      "semantic": "direct",
      "weight": 1.0
    },
    {
      "from": "__multiply_2",
      "to": "__equals_1"
    }
  ],
  "classification": {
    "kind": "algebraic"
  }
}

flowchart RL
  classDef scalar fill:#1b3a1e,stroke:#66bb6a,color:#c8e6c9,font-size:15px
  classDef vector fill:#1b3a1e,stroke:#66bb6a,color:#c8e6c9,font-size:15px
  classDef constant fill:#1b3a1e,stroke:#66bb6a,color:#c8e6c9,font-size:15px
  classDef number fill:#1b3a1e,stroke:#66bb6a,color:#c8e6c9,font-size:15px
  classDef expression fill:#1b3a1e,stroke:#66bb6a,color:#c8e6c9,font-size:15px
  classDef text fill:#1b3a1e,stroke:#66bb6a,color:#c8e6c9,font-size:15px
  classDef operator fill:#1a2740,stroke:#42a5f5,color:#bbdefb,font-size:15px
  classDef function fill:#1a2740,stroke:#42a5f5,color:#bbdefb,font-size:15px
  classDef relation fill:#332a0b,stroke:#ffa726,color:#ffe0b2,font-size:15px
  classDef result fill:#332a0b,stroke:#ffa726,color:#ffe0b2,font-size:15px
  classDef annotation fill:#131a2c,stroke:#4a5580,color:#b0bcd0,font-size:15px
  __equals_1{"="}:::relation
  E_k["$E_{k}$"]:::scalar
  __multiply_2(("$\times$")):::operator
  __power_3(("$\dfrac{1}{(\cdot)}$")):::operator
  __num_4["$2$"]:::number
  __multiply_5(("$\times$")):::operator
  m["$m$"]:::scalar
  __power_6(("${(\cdot)}^{2}$")):::operator
  v["$v$"]:::scalar
  E_k --> __equals_1
  __num_4 --> __power_3
  __power_3 -.-> __multiply_2
  m --> __multiply_5
  v --> __power_6
  __power_6 --> __multiply_5
  __multiply_5 --> __multiply_2
  __multiply_2 --> __equals_1
  linkStyle 0 stroke:#aaa,stroke-width:2px
  linkStyle 1 stroke:#aaa,stroke-width:2px
  linkStyle 2 stroke:#42a5f5,stroke-width:1px
  linkStyle 3 stroke:#ef5350,stroke-width:3px
  linkStyle 4 stroke:#aaa,stroke-width:2px
  linkStyle 5 stroke:#ef5350,stroke-width:3px
  linkStyle 6 stroke:#ef5350,stroke-width:3px
  linkStyle 7 stroke:#aaa,stroke-width:2px

{
  "nodes": [
    {
      "id": "__equals_1",
      "type": "relation",
      "op": "equals",
      "subexpr": "U = m g h",
      "chartScript": {
        "script": "U - g*h*m",
        "variables": [
          "U",
          "g",
          "h",
          "m"
        ]
      }
    },
    {
      "id": "U",
      "type": "scalar",
      "latex": "U",
      "subexpr": "U",
      "chartScript": {
        "script": "U",
        "variables": [
          "U"
        ]
      }
    },
    {
      "id": "__multiply_2",
      "type": "operator",
      "op": "multiply",
      "subexpr": "m g h",
      "chartScript": {
        "script": "g*h*m",
        "variables": [
          "g",
          "h",
          "m"
        ]
      }
    },
    {
      "id": "m",
      "type": "scalar",
      "latex": "m",
      "subexpr": "m",
      "chartScript": {
        "script": "m",
        "variables": [
          "m"
        ]
      }
    },
    {
      "id": "__multiply_3",
      "type": "operator",
      "op": "multiply",
      "subexpr": "g h",
      "chartScript": {
        "script": "g*h",
        "variables": [
          "g",
          "h"
        ]
      }
    },
    {
      "id": "g",
      "type": "scalar",
      "latex": "g",
      "subexpr": "g",
      "chartScript": {
        "script": "g",
        "variables": [
          "g"
        ]
      }
    },
    {
      "id": "h",
      "type": "scalar",
      "latex": "h",
      "subexpr": "h",
      "chartScript": {
        "script": "h",
        "variables": [
          "h"
        ]
      }
    }
  ],
  "edges": [
    {
      "from": "U",
      "to": "__equals_1"
    },
    {
      "from": "m",
      "to": "__multiply_2",
      "semantic": "direct",
      "weight": 1.0
    },
    {
      "from": "g",
      "to": "__multiply_3",
      "semantic": "direct",
      "weight": 1.0
    },
    {
      "from": "h",
      "to": "__multiply_3",
      "semantic": "direct",
      "weight": 1.0
    },
    {
      "from": "__multiply_3",
      "to": "__multiply_2",
      "semantic": "direct",
      "weight": 1.0
    },
    {
      "from": "__multiply_2",
      "to": "__equals_1"
    }
  ],
  "classification": {
    "kind": "algebraic"
  }
}

flowchart RL
  classDef scalar fill:#1b3a1e,stroke:#66bb6a,color:#c8e6c9,font-size:15px
  classDef vector fill:#1b3a1e,stroke:#66bb6a,color:#c8e6c9,font-size:15px
  classDef constant fill:#1b3a1e,stroke:#66bb6a,color:#c8e6c9,font-size:15px
  classDef number fill:#1b3a1e,stroke:#66bb6a,color:#c8e6c9,font-size:15px
  classDef expression fill:#1b3a1e,stroke:#66bb6a,color:#c8e6c9,font-size:15px
  classDef text fill:#1b3a1e,stroke:#66bb6a,color:#c8e6c9,font-size:15px
  classDef operator fill:#1a2740,stroke:#42a5f5,color:#bbdefb,font-size:15px
  classDef function fill:#1a2740,stroke:#42a5f5,color:#bbdefb,font-size:15px
  classDef relation fill:#332a0b,stroke:#ffa726,color:#ffe0b2,font-size:15px
  classDef result fill:#332a0b,stroke:#ffa726,color:#ffe0b2,font-size:15px
  classDef annotation fill:#131a2c,stroke:#4a5580,color:#b0bcd0,font-size:15px
  __equals_1{"="}:::relation
  U["$U$"]:::scalar
  __multiply_2(("$\times$")):::operator
  m["$m$"]:::scalar
  __multiply_3(("$\times$")):::operator
  g["$g$"]:::scalar
  h["$h$"]:::scalar
  U --> __equals_1
  m --> __multiply_2
  g --> __multiply_3
  h --> __multiply_3
  __multiply_3 --> __multiply_2
  __multiply_2 --> __equals_1
  linkStyle 0 stroke:#aaa,stroke-width:2px
  linkStyle 1 stroke:#ef5350,stroke-width:3px
  linkStyle 2 stroke:#ef5350,stroke-width:3px
  linkStyle 3 stroke:#ef5350,stroke-width:3px
  linkStyle 4 stroke:#ef5350,stroke-width:3px
  linkStyle 5 stroke:#aaa,stroke-width:2px

{
  "nodes": [
    {
      "id": "__equals_1",
      "type": "relation",
      "op": "equals",
      "subexpr": "W = F s \\cos\\theta",
      "chartScript": {
        "script": "-F*s*cos(theta) + W",
        "variables": [
          "F",
          "W",
          "s",
          "theta"
        ]
      }
    },
    {
      "id": "W",
      "type": "scalar",
      "latex": "W",
      "subexpr": "W",
      "chartScript": {
        "script": "W",
        "variables": [
          "W"
        ]
      }
    },
    {
      "id": "__multiply_2",
      "type": "operator",
      "op": "multiply",
      "subexpr": "F s \\cos{\\left(\\theta \\right)}",
      "chartScript": {
        "script": "F*s*cos(theta)",
        "variables": [
          "F",
          "s",
          "theta"
        ]
      }
    },
    {
      "id": "F",
      "type": "scalar",
      "latex": "F",
      "subexpr": "F",
      "chartScript": {
        "script": "F",
        "variables": [
          "F"
        ]
      }
    },
    {
      "id": "__multiply_3",
      "type": "operator",
      "op": "multiply",
      "subexpr": "s \\cos{\\left(\\theta \\right)}",
      "chartScript": {
        "script": "s*cos(theta)",
        "variables": [
          "s",
          "theta"
        ]
      }
    },
    {
      "id": "s",
      "type": "scalar",
      "latex": "s",
      "subexpr": "s",
      "chartScript": {
        "script": "s",
        "variables": [
          "s"
        ]
      }
    },
    {
      "id": "__cos_4",
      "type": "function",
      "latex": "\\cos",
      "op": "cos",
      "subexpr": "\\cos{\\left(\\theta \\right)}",
      "chartScript": {
        "script": "cos(theta)",
        "variables": [
          "theta"
        ]
      }
    },
    {
      "id": "theta",
      "type": "scalar",
      "latex": "\\theta",
      "subexpr": "\\theta",
      "chartScript": {
        "script": "theta",
        "variables": [
          "theta"
        ]
      }
    }
  ],
  "edges": [
    {
      "from": "W",
      "to": "__equals_1"
    },
    {
      "from": "F",
      "to": "__multiply_2",
      "semantic": "direct",
      "weight": 1.0
    },
    {
      "from": "s",
      "to": "__multiply_3",
      "semantic": "direct",
      "weight": 1.0
    },
    {
      "from": "theta",
      "to": "__cos_4"
    },
    {
      "from": "__cos_4",
      "to": "__multiply_3",
      "semantic": "direct",
      "weight": 1.0
    },
    {
      "from": "__multiply_3",
      "to": "__multiply_2",
      "semantic": "direct",
      "weight": 1.0
    },
    {
      "from": "__multiply_2",
      "to": "__equals_1"
    }
  ],
  "classification": {
    "kind": "algebraic"
  }
}

flowchart RL
  classDef scalar fill:#1b3a1e,stroke:#66bb6a,color:#c8e6c9,font-size:15px
  classDef vector fill:#1b3a1e,stroke:#66bb6a,color:#c8e6c9,font-size:15px
  classDef constant fill:#1b3a1e,stroke:#66bb6a,color:#c8e6c9,font-size:15px
  classDef number fill:#1b3a1e,stroke:#66bb6a,color:#c8e6c9,font-size:15px
  classDef expression fill:#1b3a1e,stroke:#66bb6a,color:#c8e6c9,font-size:15px
  classDef text fill:#1b3a1e,stroke:#66bb6a,color:#c8e6c9,font-size:15px
  classDef operator fill:#1a2740,stroke:#42a5f5,color:#bbdefb,font-size:15px
  classDef function fill:#1a2740,stroke:#42a5f5,color:#bbdefb,font-size:15px
  classDef relation fill:#332a0b,stroke:#ffa726,color:#ffe0b2,font-size:15px
  classDef result fill:#332a0b,stroke:#ffa726,color:#ffe0b2,font-size:15px
  classDef annotation fill:#131a2c,stroke:#4a5580,color:#b0bcd0,font-size:15px
  __equals_1{"="}:::relation
  W["$W$"]:::scalar
  __multiply_2(("$\times$")):::operator
  F["$F$"]:::scalar
  __multiply_3(("$\times$")):::operator
  s["$s$"]:::scalar
  __cos_4{{"$\cos(\cdot)$"}}:::function
  theta["$\theta$"]:::scalar
  W --> __equals_1
  F --> __multiply_2
  s --> __multiply_3
  theta --> __cos_4
  __cos_4 --> __multiply_3
  __multiply_3 --> __multiply_2
  __multiply_2 --> __equals_1
  linkStyle 0 stroke:#aaa,stroke-width:2px
  linkStyle 1 stroke:#ef5350,stroke-width:3px
  linkStyle 2 stroke:#ef5350,stroke-width:3px
  linkStyle 3 stroke:#aaa,stroke-width:2px
  linkStyle 4 stroke:#ef5350,stroke-width:3px
  linkStyle 5 stroke:#ef5350,stroke-width:3px
  linkStyle 6 stroke:#aaa,stroke-width:2px

{
  "nodes": [
    {
      "id": "__equals_1",
      "type": "relation",
      "op": "equals",
      "subexpr": "p = m v",
      "chartScript": {
        "script": "-m*v + p",
        "variables": [
          "m",
          "p",
          "v"
        ]
      }
    },
    {
      "id": "p",
      "type": "scalar",
      "latex": "p",
      "subexpr": "p",
      "chartScript": {
        "script": "p",
        "variables": [
          "p"
        ]
      }
    },
    {
      "id": "__multiply_2",
      "type": "operator",
      "op": "multiply",
      "subexpr": "m v",
      "chartScript": {
        "script": "m*v",
        "variables": [
          "m",
          "v"
        ]
      }
    },
    {
      "id": "m",
      "type": "scalar",
      "latex": "m",
      "subexpr": "m",
      "chartScript": {
        "script": "m",
        "variables": [
          "m"
        ]
      }
    },
    {
      "id": "v",
      "type": "scalar",
      "latex": "v",
      "subexpr": "v",
      "chartScript": {
        "script": "v",
        "variables": [
          "v"
        ]
      }
    }
  ],
  "edges": [
    {
      "from": "p",
      "to": "__equals_1"
    },
    {
      "from": "m",
      "to": "__multiply_2",
      "semantic": "direct",
      "weight": 1.0
    },
    {
      "from": "v",
      "to": "__multiply_2",
      "semantic": "direct",
      "weight": 1.0
    },
    {
      "from": "__multiply_2",
      "to": "__equals_1"
    }
  ],
  "classification": {
    "kind": "algebraic"
  }
}

flowchart RL
  classDef scalar fill:#1b3a1e,stroke:#66bb6a,color:#c8e6c9,font-size:15px
  classDef vector fill:#1b3a1e,stroke:#66bb6a,color:#c8e6c9,font-size:15px
  classDef constant fill:#1b3a1e,stroke:#66bb6a,color:#c8e6c9,font-size:15px
  classDef number fill:#1b3a1e,stroke:#66bb6a,color:#c8e6c9,font-size:15px
  classDef expression fill:#1b3a1e,stroke:#66bb6a,color:#c8e6c9,font-size:15px
  classDef text fill:#1b3a1e,stroke:#66bb6a,color:#c8e6c9,font-size:15px
  classDef operator fill:#1a2740,stroke:#42a5f5,color:#bbdefb,font-size:15px
  classDef function fill:#1a2740,stroke:#42a5f5,color:#bbdefb,font-size:15px
  classDef relation fill:#332a0b,stroke:#ffa726,color:#ffe0b2,font-size:15px
  classDef result fill:#332a0b,stroke:#ffa726,color:#ffe0b2,font-size:15px
  classDef annotation fill:#131a2c,stroke:#4a5580,color:#b0bcd0,font-size:15px
  __equals_1{"="}:::relation
  p["$p$"]:::scalar
  __multiply_2(("$\times$")):::operator
  m["$m$"]:::scalar
  v["$v$"]:::scalar
  p --> __equals_1
  m --> __multiply_2
  v --> __multiply_2
  __multiply_2 --> __equals_1
  linkStyle 0 stroke:#aaa,stroke-width:2px
  linkStyle 1 stroke:#ef5350,stroke-width:3px
  linkStyle 2 stroke:#ef5350,stroke-width:3px
  linkStyle 3 stroke:#aaa,stroke-width:2px

{
  "nodes": [
    {
      "id": "__equals_1",
      "type": "relation",
      "op": "equals",
      "subexpr": "F = G \\frac{m_1 m_2}{r^2}",
      "chartScript": {
        "script": "F - G*m_1*m_2/pow(r, 2)",
        "variables": [
          "F",
          "G",
          "m_1",
          "m_2",
          "r"
        ]
      }
    },
    {
      "id": "F",
      "type": "scalar",
      "latex": "F",
      "subexpr": "F",
      "chartScript": {
        "script": "F",
        "variables": [
          "F"
        ]
      }
    },
    {
      "id": "__multiply_2",
      "type": "operator",
      "op": "multiply",
      "subexpr": "G m_{1} m_{2} \\frac{1}{r^{2}}",
      "chartScript": {
        "script": "G*m_1*m_2/pow(r, 2)",
        "variables": [
          "G",
          "m_1",
          "m_2",
          "r"
        ]
      }
    },
    {
      "id": "G",
      "type": "scalar",
      "latex": "G",
      "subexpr": "G",
      "chartScript": {
        "script": "G",
        "variables": [
          "G"
        ]
      }
    },
    {
      "id": "__multiply_3",
      "type": "operator",
      "op": "multiply",
      "subexpr": "m_{1} m_{2} \\frac{1}{r^{2}}",
      "chartScript": {
        "script": "m_1*m_2/pow(r, 2)",
        "variables": [
          "m_1",
          "m_2",
          "r"
        ]
      }
    },
    {
      "id": "__multiply_4",
      "type": "operator",
      "op": "multiply",
      "subexpr": "m_{1} m_{2}",
      "chartScript": {
        "script": "m_1*m_2",
        "variables": [
          "m_1",
          "m_2"
        ]
      }
    },
    {
      "id": "m_1",
      "type": "scalar",
      "latex": "m_{1}",
      "subexpr": "m_{1}",
      "chartScript": {
        "script": "m_1",
        "variables": [
          "m_1"
        ]
      }
    },
    {
      "id": "m_2",
      "type": "scalar",
      "latex": "m_{2}",
      "subexpr": "m_{2}",
      "chartScript": {
        "script": "m_2",
        "variables": [
          "m_2"
        ]
      }
    },
    {
      "id": "__power_5",
      "type": "operator",
      "latex": "\\dfrac{1}{(\\cdot)}",
      "op": "power",
      "exponent": "-1",
      "subexpr": "\\frac{1}{r^{2}}",
      "chartScript": {
        "script": "pow(r, -2)",
        "variables": [
          "r"
        ]
      }
    },
    {
      "id": "__power_6",
      "type": "operator",
      "op": "power",
      "exponent": "2",
      "subexpr": "r^{2}",
      "chartScript": {
        "script": "pow(r, 2)",
        "variables": [
          "r"
        ]
      }
    },
    {
      "id": "r",
      "type": "scalar",
      "latex": "r",
      "subexpr": "r",
      "chartScript": {
        "script": "r",
        "variables": [
          "r"
        ]
      }
    }
  ],
  "edges": [
    {
      "from": "F",
      "to": "__equals_1"
    },
    {
      "from": "G",
      "to": "__multiply_2",
      "semantic": "direct",
      "weight": 1.0
    },
    {
      "from": "m_1",
      "to": "__multiply_4",
      "semantic": "direct",
      "weight": 1.0
    },
    {
      "from": "m_2",
      "to": "__multiply_4",
      "semantic": "direct",
      "weight": 1.0
    },
    {
      "from": "__multiply_4",
      "to": "__multiply_3",
      "semantic": "direct",
      "weight": 1.0
    },
    {
      "from": "r",
      "to": "__power_6"
    },
    {
      "from": "__power_6",
      "to": "__power_5"
    },
    {
      "from": "__power_5",
      "to": "__multiply_3"
    },
    {
      "from": "__multiply_3",
      "to": "__multiply_2",
      "semantic": "direct",
      "weight": 1.0
    },
    {
      "from": "__multiply_2",
      "to": "__equals_1"
    }
  ],
  "classification": {
    "kind": "algebraic"
  }
}

flowchart RL
  classDef scalar fill:#1b3a1e,stroke:#66bb6a,color:#c8e6c9,font-size:15px
  classDef vector fill:#1b3a1e,stroke:#66bb6a,color:#c8e6c9,font-size:15px
  classDef constant fill:#1b3a1e,stroke:#66bb6a,color:#c8e6c9,font-size:15px
  classDef number fill:#1b3a1e,stroke:#66bb6a,color:#c8e6c9,font-size:15px
  classDef expression fill:#1b3a1e,stroke:#66bb6a,color:#c8e6c9,font-size:15px
  classDef text fill:#1b3a1e,stroke:#66bb6a,color:#c8e6c9,font-size:15px
  classDef operator fill:#1a2740,stroke:#42a5f5,color:#bbdefb,font-size:15px
  classDef function fill:#1a2740,stroke:#42a5f5,color:#bbdefb,font-size:15px
  classDef relation fill:#332a0b,stroke:#ffa726,color:#ffe0b2,font-size:15px
  classDef result fill:#332a0b,stroke:#ffa726,color:#ffe0b2,font-size:15px
  classDef annotation fill:#131a2c,stroke:#4a5580,color:#b0bcd0,font-size:15px
  __equals_1{"="}:::relation
  F["$F$"]:::scalar
  __multiply_2(("$\times$")):::operator
  G["$G$"]:::scalar
  __multiply_3(("$\times$")):::operator
  __multiply_4(("$\times$")):::operator
  m_1["$m_{1}$"]:::scalar
  m_2["$m_{2}$"]:::scalar
  __power_5(("$\dfrac{1}{(\cdot)}$")):::operator
  __power_6(("${(\cdot)}^{2}$")):::operator
  r["$r$"]:::scalar
  F --> __equals_1
  G --> __multiply_2
  m_1 --> __multiply_4
  m_2 --> __multiply_4
  __multiply_4 --> __multiply_3
  r --> __power_6
  __power_6 --> __power_5
  __power_5 -.-> __multiply_3
  __multiply_3 --> __multiply_2
  __multiply_2 --> __equals_1
  linkStyle 0 stroke:#aaa,stroke-width:2px
  linkStyle 1 stroke:#ef5350,stroke-width:3px
  linkStyle 2 stroke:#ef5350,stroke-width:3px
  linkStyle 3 stroke:#ef5350,stroke-width:3px
  linkStyle 4 stroke:#ef5350,stroke-width:3px
  linkStyle 5 stroke:#aaa,stroke-width:2px
  linkStyle 6 stroke:#ef5350,stroke-width:6px
  linkStyle 7 stroke:#42a5f5,stroke-width:1px
  linkStyle 8 stroke:#ef5350,stroke-width:3px
  linkStyle 9 stroke:#aaa,stroke-width:2px

{
  "nodes": [
    {
      "id": "__equals_1",
      "type": "relation",
      "op": "equals",
      "subexpr": "F = \\frac{m v^2}{r}",
      "chartScript": {
        "script": "F - m*pow(v, 2)/r",
        "variables": [
          "F",
          "m",
          "r",
          "v"
        ]
      }
    },
    {
      "id": "F",
      "type": "scalar",
      "latex": "F",
      "subexpr": "F",
      "chartScript": {
        "script": "F",
        "variables": [
          "F"
        ]
      }
    },
    {
      "id": "__multiply_2",
      "type": "operator",
      "op": "multiply",
      "subexpr": "\\frac{1}{r} m v^{2}",
      "chartScript": {
        "script": "m*pow(v, 2)/r",
        "variables": [
          "m",
          "r",
          "v"
        ]
      }
    },
    {
      "id": "__multiply_3",
      "type": "operator",
      "op": "multiply",
      "subexpr": "m v^{2}",
      "chartScript": {
        "script": "m*pow(v, 2)",
        "variables": [
          "m",
          "v"
        ]
      }
    },
    {
      "id": "m",
      "type": "scalar",
      "latex": "m",
      "subexpr": "m",
      "chartScript": {
        "script": "m",
        "variables": [
          "m"
        ]
      }
    },
    {
      "id": "__power_4",
      "type": "operator",
      "op": "power",
      "exponent": "2",
      "subexpr": "v^{2}",
      "chartScript": {
        "script": "pow(v, 2)",
        "variables": [
          "v"
        ]
      }
    },
    {
      "id": "v",
      "type": "scalar",
      "latex": "v",
      "subexpr": "v",
      "chartScript": {
        "script": "v",
        "variables": [
          "v"
        ]
      }
    },
    {
      "id": "__power_5",
      "type": "operator",
      "latex": "\\dfrac{1}{(\\cdot)}",
      "op": "power",
      "exponent": "-1",
      "subexpr": "\\frac{1}{r}",
      "chartScript": {
        "script": "1/r",
        "variables": [
          "r"
        ]
      }
    },
    {
      "id": "r",
      "type": "scalar",
      "latex": "r",
      "subexpr": "r",
      "chartScript": {
        "script": "r",
        "variables": [
          "r"
        ]
      }
    }
  ],
  "edges": [
    {
      "from": "F",
      "to": "__equals_1"
    },
    {
      "from": "m",
      "to": "__multiply_3",
      "semantic": "direct",
      "weight": 1.0
    },
    {
      "from": "v",
      "to": "__power_4"
    },
    {
      "from": "__power_4",
      "to": "__multiply_3",
      "semantic": "direct",
      "weight": 1.0
    },
    {
      "from": "__multiply_3",
      "to": "__multiply_2",
      "semantic": "direct",
      "weight": 1.0
    },
    {
      "from": "r",
      "to": "__power_5"
    },
    {
      "from": "__power_5",
      "to": "__multiply_2"
    },
    {
      "from": "__multiply_2",
      "to": "__equals_1"
    }
  ],
  "classification": {
    "kind": "algebraic"
  }
}

flowchart RL
  classDef scalar fill:#1b3a1e,stroke:#66bb6a,color:#c8e6c9,font-size:15px
  classDef vector fill:#1b3a1e,stroke:#66bb6a,color:#c8e6c9,font-size:15px
  classDef constant fill:#1b3a1e,stroke:#66bb6a,color:#c8e6c9,font-size:15px
  classDef number fill:#1b3a1e,stroke:#66bb6a,color:#c8e6c9,font-size:15px
  classDef expression fill:#1b3a1e,stroke:#66bb6a,color:#c8e6c9,font-size:15px
  classDef text fill:#1b3a1e,stroke:#66bb6a,color:#c8e6c9,font-size:15px
  classDef operator fill:#1a2740,stroke:#42a5f5,color:#bbdefb,font-size:15px
  classDef function fill:#1a2740,stroke:#42a5f5,color:#bbdefb,font-size:15px
  classDef relation fill:#332a0b,stroke:#ffa726,color:#ffe0b2,font-size:15px
  classDef result fill:#332a0b,stroke:#ffa726,color:#ffe0b2,font-size:15px
  classDef annotation fill:#131a2c,stroke:#4a5580,color:#b0bcd0,font-size:15px
  __equals_1{"="}:::relation
  F["$F$"]:::scalar
  __multiply_2(("$\times$")):::operator
  __multiply_3(("$\times$")):::operator
  m["$m$"]:::scalar
  __power_4(("${(\cdot)}^{2}$")):::operator
  v["$v$"]:::scalar
  __power_5(("$\dfrac{1}{(\cdot)}$")):::operator
  r["$r$"]:::scalar
  F --> __equals_1
  m --> __multiply_3
  v --> __power_4
  __power_4 --> __multiply_3
  __multiply_3 --> __multiply_2
  r --> __power_5
  __power_5 -.-> __multiply_2
  __multiply_2 --> __equals_1
  linkStyle 0 stroke:#aaa,stroke-width:2px
  linkStyle 1 stroke:#ef5350,stroke-width:3px
  linkStyle 2 stroke:#aaa,stroke-width:2px
  linkStyle 3 stroke:#ef5350,stroke-width:3px
  linkStyle 4 stroke:#ef5350,stroke-width:3px
  linkStyle 5 stroke:#aaa,stroke-width:2px
  linkStyle 6 stroke:#42a5f5,stroke-width:1px
  linkStyle 7 stroke:#aaa,stroke-width:2px

{
  "nodes": [
    {
      "id": "__equals_1",
      "type": "relation",
      "op": "equals",
      "subexpr": "F = -k x",
      "chartScript": {
        "script": "F + k*x",
        "variables": [
          "F",
          "k",
          "x"
        ]
      }
    },
    {
      "id": "F",
      "type": "scalar",
      "latex": "F",
      "subexpr": "F",
      "chartScript": {
        "script": "F",
        "variables": [
          "F"
        ]
      }
    },
    {
      "id": "__negation_2",
      "type": "operator",
      "op": "negation",
      "subexpr": "-k x",
      "chartScript": {
        "script": "-k*x",
        "variables": [
          "k",
          "x"
        ]
      }
    },
    {
      "id": "__multiply_3",
      "type": "operator",
      "op": "multiply",
      "subexpr": "k x",
      "chartScript": {
        "script": "k*x",
        "variables": [
          "k",
          "x"
        ]
      }
    },
    {
      "id": "k",
      "type": "scalar",
      "latex": "k",
      "subexpr": "k",
      "chartScript": {
        "script": "k",
        "variables": [
          "k"
        ]
      }
    },
    {
      "id": "x",
      "type": "scalar",
      "latex": "x",
      "subexpr": "x",
      "chartScript": {
        "script": "x",
        "variables": [
          "x"
        ]
      }
    }
  ],
  "edges": [
    {
      "from": "F",
      "to": "__equals_1"
    },
    {
      "from": "k",
      "to": "__multiply_3",
      "semantic": "direct",
      "weight": 1.0
    },
    {
      "from": "x",
      "to": "__multiply_3",
      "semantic": "direct",
      "weight": 1.0
    },
    {
      "from": "__multiply_3",
      "to": "__negation_2"
    },
    {
      "from": "__negation_2",
      "to": "__equals_1"
    }
  ],
  "classification": {
    "kind": "algebraic"
  }
}

flowchart RL
  classDef scalar fill:#1b3a1e,stroke:#66bb6a,color:#c8e6c9,font-size:15px
  classDef vector fill:#1b3a1e,stroke:#66bb6a,color:#c8e6c9,font-size:15px
  classDef constant fill:#1b3a1e,stroke:#66bb6a,color:#c8e6c9,font-size:15px
  classDef number fill:#1b3a1e,stroke:#66bb6a,color:#c8e6c9,font-size:15px
  classDef expression fill:#1b3a1e,stroke:#66bb6a,color:#c8e6c9,font-size:15px
  classDef text fill:#1b3a1e,stroke:#66bb6a,color:#c8e6c9,font-size:15px
  classDef operator fill:#1a2740,stroke:#42a5f5,color:#bbdefb,font-size:15px
  classDef function fill:#1a2740,stroke:#42a5f5,color:#bbdefb,font-size:15px
  classDef relation fill:#332a0b,stroke:#ffa726,color:#ffe0b2,font-size:15px
  classDef result fill:#332a0b,stroke:#ffa726,color:#ffe0b2,font-size:15px
  classDef annotation fill:#131a2c,stroke:#4a5580,color:#b0bcd0,font-size:15px
  __equals_1{"="}:::relation
  F["$F$"]:::scalar
  __negation_2@{ shape: "flip-tri", label: "$-$" }
  __multiply_3(("$\times$")):::operator
  k["$k$"]:::scalar
  x["$x$"]:::scalar
  class __negation_2 operator
  F --> __equals_1
  k --> __multiply_3
  x --> __multiply_3
  __multiply_3 --> __negation_2
  __negation_2 --> __equals_1
  linkStyle 0 stroke:#aaa,stroke-width:2px
  linkStyle 1 stroke:#ef5350,stroke-width:3px
  linkStyle 2 stroke:#ef5350,stroke-width:3px
  linkStyle 3 stroke:#aaa,stroke-width:2px
  linkStyle 4 stroke:#aaa,stroke-width:2px

{
  "nodes": [
    {
      "id": "__equals_1",
      "type": "relation",
      "op": "equals",
      "subexpr": "P = \\frac{W}{t}",
      "chartScript": {
        "script": "P - W/t",
        "variables": [
          "P",
          "W",
          "t"
        ]
      }
    },
    {
      "id": "P",
      "type": "scalar",
      "latex": "P",
      "subexpr": "P",
      "chartScript": {
        "script": "P",
        "variables": [
          "P"
        ]
      }
    },
    {
      "id": "__multiply_2",
      "type": "operator",
      "op": "multiply",
      "subexpr": "W \\frac{1}{t}",
      "chartScript": {
        "script": "W/t",
        "variables": [
          "W",
          "t"
        ]
      }
    },
    {
      "id": "W",
      "type": "scalar",
      "latex": "W",
      "subexpr": "W",
      "chartScript": {
        "script": "W",
        "variables": [
          "W"
        ]
      }
    },
    {
      "id": "__power_3",
      "type": "operator",
      "latex": "\\dfrac{1}{(\\cdot)}",
      "op": "power",
      "exponent": "-1",
      "subexpr": "\\frac{1}{t}",
      "chartScript": {
        "script": "1/t",
        "variables": [
          "t"
        ]
      }
    },
    {
      "id": "t",
      "type": "scalar",
      "latex": "t",
      "subexpr": "t",
      "chartScript": {
        "script": "t",
        "variables": [
          "t"
        ]
      }
    }
  ],
  "edges": [
    {
      "from": "P",
      "to": "__equals_1"
    },
    {
      "from": "W",
      "to": "__multiply_2",
      "semantic": "direct",
      "weight": 1.0
    },
    {
      "from": "t",
      "to": "__power_3"
    },
    {
      "from": "__power_3",
      "to": "__multiply_2"
    },
    {
      "from": "__multiply_2",
      "to": "__equals_1"
    }
  ],
  "classification": {
    "kind": "algebraic"
  }
}

flowchart RL
  classDef scalar fill:#1b3a1e,stroke:#66bb6a,color:#c8e6c9,font-size:15px
  classDef vector fill:#1b3a1e,stroke:#66bb6a,color:#c8e6c9,font-size:15px
  classDef constant fill:#1b3a1e,stroke:#66bb6a,color:#c8e6c9,font-size:15px
  classDef number fill:#1b3a1e,stroke:#66bb6a,color:#c8e6c9,font-size:15px
  classDef expression fill:#1b3a1e,stroke:#66bb6a,color:#c8e6c9,font-size:15px
  classDef text fill:#1b3a1e,stroke:#66bb6a,color:#c8e6c9,font-size:15px
  classDef operator fill:#1a2740,stroke:#42a5f5,color:#bbdefb,font-size:15px
  classDef function fill:#1a2740,stroke:#42a5f5,color:#bbdefb,font-size:15px
  classDef relation fill:#332a0b,stroke:#ffa726,color:#ffe0b2,font-size:15px
  classDef result fill:#332a0b,stroke:#ffa726,color:#ffe0b2,font-size:15px
  classDef annotation fill:#131a2c,stroke:#4a5580,color:#b0bcd0,font-size:15px
  __equals_1{"="}:::relation
  P["$P$"]:::scalar
  __multiply_2(("$\times$")):::operator
  W["$W$"]:::scalar
  __power_3(("$\dfrac{1}{(\cdot)}$")):::operator
  t["$t$"]:::scalar
  P --> __equals_1
  W --> __multiply_2
  t --> __power_3
  __power_3 -.-> __multiply_2
  __multiply_2 --> __equals_1
  linkStyle 0 stroke:#aaa,stroke-width:2px
  linkStyle 1 stroke:#ef5350,stroke-width:3px
  linkStyle 2 stroke:#aaa,stroke-width:2px
  linkStyle 3 stroke:#42a5f5,stroke-width:1px
  linkStyle 4 stroke:#aaa,stroke-width:2px

{
  "nodes": [
    {
      "id": "__equals_1",
      "type": "relation",
      "op": "equals",
      "subexpr": "L = T - V",
      "chartScript": {
        "script": "L - T + V",
        "variables": [
          "L",
          "T",
          "V"
        ]
      }
    },
    {
      "id": "L",
      "type": "scalar",
      "latex": "L",
      "subexpr": "L",
      "chartScript": {
        "script": "L",
        "variables": [
          "L"
        ]
      }
    },
    {
      "id": "__add_2",
      "type": "operator",
      "op": "add",
      "subexpr": "T - V",
      "chartScript": {
        "script": "T - V",
        "variables": [
          "T",
          "V"
        ]
      }
    },
    {
      "id": "T",
      "type": "scalar",
      "latex": "T",
      "subexpr": "T",
      "chartScript": {
        "script": "T",
        "variables": [
          "T"
        ]
      }
    },
    {
      "id": "__negation_3",
      "type": "operator",
      "op": "negation",
      "subexpr": "-V",
      "chartScript": {
        "script": "-V",
        "variables": [
          "V"
        ]
      }
    },
    {
      "id": "V",
      "type": "scalar",
      "latex": "V",
      "subexpr": "V",
      "chartScript": {
        "script": "V",
        "variables": [
          "V"
        ]
      }
    }
  ],
  "edges": [
    {
      "from": "L",
      "to": "__equals_1"
    },
    {
      "from": "T",
      "to": "__add_2"
    },
    {
      "from": "V",
      "to": "__negation_3"
    },
    {
      "from": "__negation_3",
      "to": "__add_2"
    },
    {
      "from": "__add_2",
      "to": "__equals_1"
    }
  ],
  "classification": {
    "kind": "algebraic"
  }
}

flowchart RL
  classDef scalar fill:#1b3a1e,stroke:#66bb6a,color:#c8e6c9,font-size:15px
  classDef vector fill:#1b3a1e,stroke:#66bb6a,color:#c8e6c9,font-size:15px
  classDef constant fill:#1b3a1e,stroke:#66bb6a,color:#c8e6c9,font-size:15px
  classDef number fill:#1b3a1e,stroke:#66bb6a,color:#c8e6c9,font-size:15px
  classDef expression fill:#1b3a1e,stroke:#66bb6a,color:#c8e6c9,font-size:15px
  classDef text fill:#1b3a1e,stroke:#66bb6a,color:#c8e6c9,font-size:15px
  classDef operator fill:#1a2740,stroke:#42a5f5,color:#bbdefb,font-size:15px
  classDef function fill:#1a2740,stroke:#42a5f5,color:#bbdefb,font-size:15px
  classDef relation fill:#332a0b,stroke:#ffa726,color:#ffe0b2,font-size:15px
  classDef result fill:#332a0b,stroke:#ffa726,color:#ffe0b2,font-size:15px
  classDef annotation fill:#131a2c,stroke:#4a5580,color:#b0bcd0,font-size:15px
  __equals_1{"="}:::relation
  L["$L$"]:::scalar
  __add_2(("$+$")):::operator
  T["$T$"]:::scalar
  __negation_3@{ shape: "flip-tri", label: "$-$" }
  V["$V$"]:::scalar
  class __negation_3 operator
  L --> __equals_1
  T --> __add_2
  V --> __negation_3
  __negation_3 --> __add_2
  __add_2 --> __equals_1
  linkStyle 0 stroke:#aaa,stroke-width:2px
  linkStyle 1 stroke:#aaa,stroke-width:2px
  linkStyle 2 stroke:#aaa,stroke-width:2px
  linkStyle 3 stroke:#aaa,stroke-width:2px
  linkStyle 4 stroke:#aaa,stroke-width:2px

{
  "nodes": [
    {
      "id": "__equals_1",
      "type": "relation",
      "op": "equals",
      "subexpr": "\\frac{d}{dt} \\frac{\\partial L}{\\partial \\dot{q}} - \\frac{\\partial L}{\\partial q} = 0",
      "chartScript": {
        "script": "0",
        "variables": []
      }
    },
    {
      "id": "__add_2",
      "type": "operator",
      "op": "add",
      "subexpr": "-\\frac{\\partial L}{\\partial q} + \\frac{\\partial}{\\partial t} \\frac{L \\partial}{\\partial \\dot{q}}",
      "chartScript": {
        "script": "0",
        "variables": []
      }
    },
    {
      "id": "__multiply_4",
      "type": "operator",
      "op": "multiply",
      "subexpr": "\\partial L \\frac{1}{\\partial \\dot{q}}",
      "chartScript": {
        "script": "L/(dot*q)",
        "variables": [
          "L",
          "dot",
          "q"
        ]
      }
    },
    {
      "id": "__multiply_5",
      "type": "operator",
      "op": "multiply",
      "subexpr": "\\partial L",
      "chartScript": {
        "script": "L*partial",
        "variables": [
          "L",
          "partial"
        ]
      }
    },
    {
      "id": "partial",
      "type": "scalar",
      "latex": "\\partial",
      "subexpr": "\\partial",
      "chartScript": {
        "script": "partial",
        "variables": [
          "partial"
        ]
      }
    },
    {
      "id": "L",
      "type": "scalar",
      "latex": "L",
      "subexpr": "L",
      "chartScript": {
        "script": "L",
        "variables": [
          "L"
        ]
      }
    },
    {
      "id": "__power_6",
      "type": "operator",
      "latex": "\\dfrac{1}{(\\cdot)}",
      "op": "power",
      "exponent": "-1",
      "subexpr": "\\frac{1}{\\partial \\dot{q}}",
      "chartScript": {
        "script": "1/(dot*partial*q)",
        "variables": [
          "dot",
          "partial",
          "q"
        ]
      }
    },
    {
      "id": "__multiply_7",
      "type": "operator",
      "op": "multiply",
      "subexpr": "\\partial \\dot{q}",
      "chartScript": {
        "script": "dot*partial*q",
        "variables": [
          "dot",
          "partial",
          "q"
        ]
      }
    },
    {
      "id": "q",
      "type": "scalar",
      "latex": "q",
      "subexpr": "q",
      "chartScript": {
        "script": "q",
        "variables": [
          "q"
        ]
      }
    },
    {
      "id": "t",
      "type": "scalar",
      "latex": "t",
      "subexpr": "t",
      "chartScript": {
        "script": "t",
        "variables": [
          "t"
        ]
      }
    },
    {
      "id": "__deriv_8",
      "type": "operator",
      "op": "derivative",
      "with_respect_to": "t",
      "subexpr": "\\dot{q}",
      "chartScript": {
        "script": "dot*q",
        "variables": [
          "dot",
          "q"
        ]
      }
    },
    {
      "id": "__deriv_3",
      "type": "operator",
      "op": "derivative",
      "with_respect_to": "t",
      "subexpr": "\\frac{\\partial}{\\partial t} \\frac{L \\partial}{\\partial \\dot{q}}",
      "chartScript": {
        "script": "0",
        "variables": []
      }
    },
    {
      "id": "__negation_9",
      "type": "operator",
      "op": "negation",
      "subexpr": "-\\frac{\\partial L}{\\partial q}",
      "chartScript": {
        "script": "0",
        "variables": []
      }
    },
    {
      "id": "__deriv_10",
      "type": "operator",
      "op": "partial_derivative",
      "with_respect_to": "q",
      "subexpr": "\\frac{\\partial L}{\\partial q}",
      "chartScript": {
        "script": "0",
        "variables": []
      }
    },
    {
      "id": "__num_11",
      "type": "number",
      "label": "0",
      "subexpr": "0",
      "chartScript": {
        "script": "0",
        "variables": []
      }
    }
  ],
  "edges": [
    {
      "from": "partial",
      "to": "__multiply_5",
      "semantic": "direct",
      "weight": 1.0
    },
    {
      "from": "L",
      "to": "__multiply_5",
      "semantic": "direct",
      "weight": 1.0
    },
    {
      "from": "__multiply_5",
      "to": "__multiply_4",
      "semantic": "direct",
      "weight": 1.0
    },
    {
      "from": "partial",
      "to": "__multiply_7",
      "semantic": "direct",
      "weight": 1.0
    },
    {
      "from": "q",
      "to": "__deriv_8"
    },
    {
      "from": "t",
      "to": "__deriv_8",
      "role": "wrt"
    },
    {
      "from": "__deriv_8",
      "to": "__multiply_7",
      "semantic": "direct",
      "weight": 1.0
    },
    {
      "from": "__multiply_7",
      "to": "__power_6"
    },
    {
      "from": "__power_6",
      "to": "__multiply_4"
    },
    {
      "from": "__multiply_4",
      "to": "__deriv_3"
    },
    {
      "from": "t",
      "to": "__deriv_3",
      "role": "wrt"
    },
    {
      "from": "__deriv_3",
      "to": "__add_2"
    },
    {
      "from": "L",
      "to": "__deriv_10"
    },
    {
      "from": "q",
      "to": "__deriv_10",
      "role": "wrt"
    },
    {
      "from": "__deriv_10",
      "to": "__negation_9"
    },
    {
      "from": "__negation_9",
      "to": "__add_2"
    },
    {
      "from": "__add_2",
      "to": "__equals_1"
    },
    {
      "from": "__num_11",
      "to": "__equals_1"
    }
  ],
  "classification": {
    "kind": "PDE",
    "order": 1,
    "dependent_variables": [
      "L",
      "q"
    ],
    "independent_variables": [
      "q",
      "t"
    ]
  }
}

flowchart RL
  classDef scalar fill:#1b3a1e,stroke:#66bb6a,color:#c8e6c9,font-size:15px
  classDef vector fill:#1b3a1e,stroke:#66bb6a,color:#c8e6c9,font-size:15px
  classDef constant fill:#1b3a1e,stroke:#66bb6a,color:#c8e6c9,font-size:15px
  classDef number fill:#1b3a1e,stroke:#66bb6a,color:#c8e6c9,font-size:15px
  classDef expression fill:#1b3a1e,stroke:#66bb6a,color:#c8e6c9,font-size:15px
  classDef text fill:#1b3a1e,stroke:#66bb6a,color:#c8e6c9,font-size:15px
  classDef operator fill:#1a2740,stroke:#42a5f5,color:#bbdefb,font-size:15px
  classDef function fill:#1a2740,stroke:#42a5f5,color:#bbdefb,font-size:15px
  classDef relation fill:#332a0b,stroke:#ffa726,color:#ffe0b2,font-size:15px
  classDef result fill:#332a0b,stroke:#ffa726,color:#ffe0b2,font-size:15px
  classDef annotation fill:#131a2c,stroke:#4a5580,color:#b0bcd0,font-size:15px
  __equals_1{"="}:::relation
  __add_2(("$+$")):::operator
  __multiply_4(("$\times$")):::operator
  __multiply_5(("$\times$")):::operator
  partial["$\partial$"]:::scalar
  L["$L$"]:::scalar
  __power_6(("$\dfrac{1}{(\cdot)}$")):::operator
  __multiply_7(("$\times$")):::operator
  q["$q$"]:::scalar
  t["$t$"]:::scalar
  __deriv_8(("$\dfrac{d}{d t}$")):::operator
  __deriv_3(("$\dfrac{d}{d t}$")):::operator
  __negation_9@{ shape: "flip-tri", label: "$-$" }
  __deriv_10(("$\dfrac{\partial}{\partial q}$")):::operator
  __num_11["$0$"]:::number
  class __negation_9 operator
  partial --> __multiply_5
  L --> __multiply_5
  __multiply_5 --> __multiply_4
  partial --> __multiply_7
  q --> __deriv_8
  t -->|wrt| __deriv_8
  __deriv_8 --> __multiply_7
  __multiply_7 --> __power_6
  __power_6 -.-> __multiply_4
  __multiply_4 --> __deriv_3
  t -->|wrt| __deriv_3
  __deriv_3 --> __add_2
  L --> __deriv_10
  q -->|wrt| __deriv_10
  __deriv_10 --> __negation_9
  __negation_9 --> __add_2
  __add_2 --> __equals_1
  __num_11 --> __equals_1
  linkStyle 0 stroke:#ef5350,stroke-width:3px
  linkStyle 1 stroke:#ef5350,stroke-width:3px
  linkStyle 2 stroke:#ef5350,stroke-width:3px
  linkStyle 3 stroke:#ef5350,stroke-width:3px
  linkStyle 4 stroke:#aaa,stroke-width:2px
  linkStyle 5 stroke:#aaa,stroke-width:2px
  linkStyle 6 stroke:#ef5350,stroke-width:3px
  linkStyle 7 stroke:#aaa,stroke-width:2px
  linkStyle 8 stroke:#42a5f5,stroke-width:1px
  linkStyle 9 stroke:#aaa,stroke-width:2px
  linkStyle 10 stroke:#aaa,stroke-width:2px
  linkStyle 11 stroke:#aaa,stroke-width:2px
  linkStyle 12 stroke:#aaa,stroke-width:2px
  linkStyle 13 stroke:#aaa,stroke-width:2px
  linkStyle 14 stroke:#aaa,stroke-width:2px
  linkStyle 15 stroke:#aaa,stroke-width:2px
  linkStyle 16 stroke:#aaa,stroke-width:2px
  linkStyle 17 stroke:#aaa,stroke-width:2px

{
  "nodes": [
    {
      "id": "__equals_1",
      "type": "relation",
      "op": "equals",
      "subexpr": "H = T + V",
      "chartScript": {
        "script": "H - T - V",
        "variables": [
          "H",
          "T",
          "V"
        ]
      }
    },
    {
      "id": "H",
      "type": "scalar",
      "latex": "H",
      "subexpr": "H",
      "chartScript": {
        "script": "H",
        "variables": [
          "H"
        ]
      }
    },
    {
      "id": "__add_2",
      "type": "operator",
      "op": "add",
      "subexpr": "T + V",
      "chartScript": {
        "script": "T + V",
        "variables": [
          "T",
          "V"
        ]
      }
    },
    {
      "id": "T",
      "type": "scalar",
      "latex": "T",
      "subexpr": "T",
      "chartScript": {
        "script": "T",
        "variables": [
          "T"
        ]
      }
    },
    {
      "id": "V",
      "type": "scalar",
      "latex": "V",
      "subexpr": "V",
      "chartScript": {
        "script": "V",
        "variables": [
          "V"
        ]
      }
    }
  ],
  "edges": [
    {
      "from": "H",
      "to": "__equals_1"
    },
    {
      "from": "T",
      "to": "__add_2"
    },
    {
      "from": "V",
      "to": "__add_2"
    },
    {
      "from": "__add_2",
      "to": "__equals_1"
    }
  ],
  "classification": {
    "kind": "algebraic"
  }
}

flowchart RL
  classDef scalar fill:#1b3a1e,stroke:#66bb6a,color:#c8e6c9,font-size:15px
  classDef vector fill:#1b3a1e,stroke:#66bb6a,color:#c8e6c9,font-size:15px
  classDef constant fill:#1b3a1e,stroke:#66bb6a,color:#c8e6c9,font-size:15px
  classDef number fill:#1b3a1e,stroke:#66bb6a,color:#c8e6c9,font-size:15px
  classDef expression fill:#1b3a1e,stroke:#66bb6a,color:#c8e6c9,font-size:15px
  classDef text fill:#1b3a1e,stroke:#66bb6a,color:#c8e6c9,font-size:15px
  classDef operator fill:#1a2740,stroke:#42a5f5,color:#bbdefb,font-size:15px
  classDef function fill:#1a2740,stroke:#42a5f5,color:#bbdefb,font-size:15px
  classDef relation fill:#332a0b,stroke:#ffa726,color:#ffe0b2,font-size:15px
  classDef result fill:#332a0b,stroke:#ffa726,color:#ffe0b2,font-size:15px
  classDef annotation fill:#131a2c,stroke:#4a5580,color:#b0bcd0,font-size:15px
  __equals_1{"="}:::relation
  H["$H$"]:::scalar
  __add_2(("$+$")):::operator
  T["$T$"]:::scalar
  V["$V$"]:::scalar
  H --> __equals_1
  T --> __add_2
  V --> __add_2
  __add_2 --> __equals_1
  linkStyle 0 stroke:#aaa,stroke-width:2px
  linkStyle 1 stroke:#aaa,stroke-width:2px
  linkStyle 2 stroke:#aaa,stroke-width:2px
  linkStyle 3 stroke:#aaa,stroke-width:2px

{
  "nodes": [
    {
      "id": "__equals_1",
      "type": "relation",
      "op": "equals",
      "subexpr": "L = I \\omega",
      "chartScript": {
        "script": "-I*omega + L",
        "variables": [
          "I",
          "L",
          "omega"
        ]
      }
    },
    {
      "id": "L",
      "type": "scalar",
      "latex": "L",
      "subexpr": "L",
      "chartScript": {
        "script": "L",
        "variables": [
          "L"
        ]
      }
    },
    {
      "id": "__multiply_2",
      "type": "operator",
      "op": "multiply",
      "subexpr": "I \\omega",
      "chartScript": {
        "script": "I*omega",
        "variables": [
          "I",
          "omega"
        ]
      }
    },
    {
      "id": "I",
      "type": "scalar",
      "latex": "I",
      "subexpr": "I",
      "chartScript": {
        "script": "I",
        "variables": [
          "I"
        ]
      }
    },
    {
      "id": "omega",
      "type": "scalar",
      "latex": "\\omega",
      "subexpr": "\\omega",
      "chartScript": {
        "script": "omega",
        "variables": [
          "omega"
        ]
      }
    }
  ],
  "edges": [
    {
      "from": "L",
      "to": "__equals_1"
    },
    {
      "from": "I",
      "to": "__multiply_2",
      "semantic": "direct",
      "weight": 1.0
    },
    {
      "from": "omega",
      "to": "__multiply_2",
      "semantic": "direct",
      "weight": 1.0
    },
    {
      "from": "__multiply_2",
      "to": "__equals_1"
    }
  ],
  "classification": {
    "kind": "algebraic"
  }
}

flowchart RL
  classDef scalar fill:#1b3a1e,stroke:#66bb6a,color:#c8e6c9,font-size:15px
  classDef vector fill:#1b3a1e,stroke:#66bb6a,color:#c8e6c9,font-size:15px
  classDef constant fill:#1b3a1e,stroke:#66bb6a,color:#c8e6c9,font-size:15px
  classDef number fill:#1b3a1e,stroke:#66bb6a,color:#c8e6c9,font-size:15px
  classDef expression fill:#1b3a1e,stroke:#66bb6a,color:#c8e6c9,font-size:15px
  classDef text fill:#1b3a1e,stroke:#66bb6a,color:#c8e6c9,font-size:15px
  classDef operator fill:#1a2740,stroke:#42a5f5,color:#bbdefb,font-size:15px
  classDef function fill:#1a2740,stroke:#42a5f5,color:#bbdefb,font-size:15px
  classDef relation fill:#332a0b,stroke:#ffa726,color:#ffe0b2,font-size:15px
  classDef result fill:#332a0b,stroke:#ffa726,color:#ffe0b2,font-size:15px
  classDef annotation fill:#131a2c,stroke:#4a5580,color:#b0bcd0,font-size:15px
  __equals_1{"="}:::relation
  L["$L$"]:::scalar
  __multiply_2(("$\times$")):::operator
  I["$I$"]:::scalar
  omega["$\omega$"]:::scalar
  L --> __equals_1
  I --> __multiply_2
  omega --> __multiply_2
  __multiply_2 --> __equals_1
  linkStyle 0 stroke:#aaa,stroke-width:2px
  linkStyle 1 stroke:#ef5350,stroke-width:3px
  linkStyle 2 stroke:#ef5350,stroke-width:3px
  linkStyle 3 stroke:#aaa,stroke-width:2px

{
  "nodes": [
    {
      "id": "__equals_1",
      "type": "relation",
      "op": "equals",
      "subexpr": "\\tau = r F \\sin\\theta",
      "chartScript": {
        "script": "-F*r*sin(theta) + tau",
        "variables": [
          "F",
          "r",
          "tau",
          "theta"
        ]
      }
    },
    {
      "id": "tau",
      "type": "scalar",
      "latex": "\\tau",
      "subexpr": "\\tau",
      "chartScript": {
        "script": "tau",
        "variables": [
          "tau"
        ]
      }
    },
    {
      "id": "__multiply_2",
      "type": "operator",
      "op": "multiply",
      "subexpr": "r F \\sin{\\left(\\theta \\right)}",
      "chartScript": {
        "script": "F*r*sin(theta)",
        "variables": [
          "F",
          "r",
          "theta"
        ]
      }
    },
    {
      "id": "r",
      "type": "scalar",
      "latex": "r",
      "subexpr": "r",
      "chartScript": {
        "script": "r",
        "variables": [
          "r"
        ]
      }
    },
    {
      "id": "__multiply_3",
      "type": "operator",
      "op": "multiply",
      "subexpr": "F \\sin{\\left(\\theta \\right)}",
      "chartScript": {
        "script": "F*sin(theta)",
        "variables": [
          "F",
          "theta"
        ]
      }
    },
    {
      "id": "F",
      "type": "scalar",
      "latex": "F",
      "subexpr": "F",
      "chartScript": {
        "script": "F",
        "variables": [
          "F"
        ]
      }
    },
    {
      "id": "__sin_4",
      "type": "function",
      "latex": "\\sin",
      "op": "sin",
      "subexpr": "\\sin{\\left(\\theta \\right)}",
      "chartScript": {
        "script": "sin(theta)",
        "variables": [
          "theta"
        ]
      }
    },
    {
      "id": "theta",
      "type": "scalar",
      "latex": "\\theta",
      "subexpr": "\\theta",
      "chartScript": {
        "script": "theta",
        "variables": [
          "theta"
        ]
      }
    }
  ],
  "edges": [
    {
      "from": "tau",
      "to": "__equals_1"
    },
    {
      "from": "r",
      "to": "__multiply_2",
      "semantic": "direct",
      "weight": 1.0
    },
    {
      "from": "F",
      "to": "__multiply_3",
      "semantic": "direct",
      "weight": 1.0
    },
    {
      "from": "theta",
      "to": "__sin_4"
    },
    {
      "from": "__sin_4",
      "to": "__multiply_3",
      "semantic": "direct",
      "weight": 1.0
    },
    {
      "from": "__multiply_3",
      "to": "__multiply_2",
      "semantic": "direct",
      "weight": 1.0
    },
    {
      "from": "__multiply_2",
      "to": "__equals_1"
    }
  ],
  "classification": {
    "kind": "algebraic"
  }
}

flowchart RL
  classDef scalar fill:#1b3a1e,stroke:#66bb6a,color:#c8e6c9,font-size:15px
  classDef vector fill:#1b3a1e,stroke:#66bb6a,color:#c8e6c9,font-size:15px
  classDef constant fill:#1b3a1e,stroke:#66bb6a,color:#c8e6c9,font-size:15px
  classDef number fill:#1b3a1e,stroke:#66bb6a,color:#c8e6c9,font-size:15px
  classDef expression fill:#1b3a1e,stroke:#66bb6a,color:#c8e6c9,font-size:15px
  classDef text fill:#1b3a1e,stroke:#66bb6a,color:#c8e6c9,font-size:15px
  classDef operator fill:#1a2740,stroke:#42a5f5,color:#bbdefb,font-size:15px
  classDef function fill:#1a2740,stroke:#42a5f5,color:#bbdefb,font-size:15px
  classDef relation fill:#332a0b,stroke:#ffa726,color:#ffe0b2,font-size:15px
  classDef result fill:#332a0b,stroke:#ffa726,color:#ffe0b2,font-size:15px
  classDef annotation fill:#131a2c,stroke:#4a5580,color:#b0bcd0,font-size:15px
  __equals_1{"="}:::relation
  tau["$\tau$"]:::scalar
  __multiply_2(("$\times$")):::operator
  r["$r$"]:::scalar
  __multiply_3(("$\times$")):::operator
  F["$F$"]:::scalar
  __sin_4{{"$\sin(\cdot)$"}}:::function
  theta["$\theta$"]:::scalar
  tau --> __equals_1
  r --> __multiply_2
  F --> __multiply_3
  theta --> __sin_4
  __sin_4 --> __multiply_3
  __multiply_3 --> __multiply_2
  __multiply_2 --> __equals_1
  linkStyle 0 stroke:#aaa,stroke-width:2px
  linkStyle 1 stroke:#ef5350,stroke-width:3px
  linkStyle 2 stroke:#ef5350,stroke-width:3px
  linkStyle 3 stroke:#aaa,stroke-width:2px
  linkStyle 4 stroke:#ef5350,stroke-width:3px
  linkStyle 5 stroke:#ef5350,stroke-width:3px
  linkStyle 6 stroke:#aaa,stroke-width:2px