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The Principia Machina/UWC/RP1/TFK/TPK

From The Invariance Itself
Revision as of 23:12, 7 October 2026 by TPX (talk | contribs) (TPX: TFK/TPK for RP1)
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{
  "ASSUMPTION": [
    {
      "NAME": "A_gpos",
      "PROPOSITION": "g is positive",
      "REFS": [
        "g"
      ]
    },
    {
      "NAME": "A_lpos",
      "PROPOSITION": "l is positive",
      "REFS": [
        "l"
      ]
    }
  ],
  "BOUNDARY": [
    {
      "CONDITION": "abs(theta) < theta_max",
      "NAME": "B_small",
      "PREDICATE": "|theta| < theta_max",
      "REFS": [
        "theta",
        "theta_max"
      ]
    }
  ],
  "CONSTANT": [
    {
      "DIMENSION": "L1 T-2",
      "NAME": "g",
      "UNCERTAINTY": "0.00001",
      "UNIT": "m s-2",
      "VALUE": "9.80665"
    },
    {
      "DIMENSION": "L1",
      "NAME": "l",
      "UNCERTAINTY": "0.001",
      "UNIT": "m",
      "VALUE": "1.0"
    },
    {
      "DIMENSION": "1",
      "NAME": "theta_max",
      "UNCERTAINTY": "0.005",
      "UNIT": "rad",
      "VALUE": "0.1"
    }
  ],
  "CONSTRAINT": [
    {
      "ACTION": "FIX",
      "NAME": "C_NOZ",
      "STATEMENT": "motion is restricted to vertical plane: z = 0",
      "TARGET": "z",
      "UNIT": "m",
      "VALUE": "0"
    }
  ],
  "DOF": [
    {
      "DIMENSION": "T1",
      "NAME": "t"
    },
    {
      "DIMENSION": "1",
      "NAME": "theta"
    },
    {
      "DIMENSION": "T-1",
      "NAME": "omega"
    },
    {
      "DIMENSION": "L1",
      "NAME": "z"
    }
  ],
  "LAW": [
    {
      "EQUATION": "D(omega, t) = -g / l * theta",
      "NAME": "EOM_THETA",
      "REFS": [
        "omega",
        "t",
        "g",
        "l",
        "theta"
      ],
      "ROLE": "EOM(omega)",
      "STATEMENT": "d omega/dt = -(g/l) theta"
    },
    {
      "EQUATION": "D(theta, t) = omega",
      "NAME": "KIN",
      "REFS": [
        "theta",
        "omega",
        "t"
      ],
      "ROLE": "EOM(theta)",
      "STATEMENT": "d theta/dt = omega"
    },
    {
      "EQUATION": "D(z, t, 2) = 0",
      "NAME": "EOM_Z",
      "REFS": [
        "z",
        "t"
      ],
      "ROLE": "CONSTRAINT",
      "STATEMENT": "d2z/dt2 = 0"
    }
  ]
}