View source for The Principia Machina/TPC-PY/examples/spring mistakes form boundary.json

{
  "TPK": {
    "DOF": [
      {"NAME": "t", "DIMENSION": "T1"},
      {"NAME": "x", "DIMENSION": "L1"},
      {"NAME": "v", "DIMENSION": "L1 T-1"},
      {"NAME": "z", "DIMENSION": "L1"}
    ],
    "CONSTANT": [
      {"NAME": "m", "DIMENSION": "M1"},
      {"NAME": "k_s", "DIMENSION": "M1 T-2"},
      {
        "NAME": "x_max",
        "DIMENSION": "L1",
        "VALUE": "0.05",
        "UNIT": "m",
        "UNCERTAINTY": "0.001"
      }
    ],
    "LAW": [
      {
        "NAME": "EOM_X",
        "STATEMENT": "m dv/dt = -k_s x",
        "REFS": ["m", "v", "k_s", "x", "t"],
        "ROLE": "EOM(v)",
        "EQUATION": "m * D(v, t) = -k_s * x"
      },
      {
        "NAME": "KIN",
        "STATEMENT": "dx/dt = v",
        "REFS": ["x", "v", "t"],
        "ROLE": "EOM(x)",
        "EQUATION": "D(x, t) = v"
      },
      {
        "NAME": "EOM_Z",
        "STATEMENT": "m d2z/dt2 = 0",
        "REFS": ["m", "z", "t"],
        "ROLE": "CONSTRAINT",
        "EQUATION": "m * D(z, t, 2) = 0"
      }
    ],
    "ASSUMPTION": [
      {
        "NAME": "A_kpos",
        "PROPOSITION": "k_s is positive",
        "REFS": ["k_s"]
      },
      {
        "NAME": "A_mpos",
        "PROPOSITION": "m is positive",
        "REFS": ["m"]
      }
    ],
    "CONSTRAINT": [
      {
        "NAME": "C_NOZ",
        "TARGET": "z",
        "ACTION": "FIX",
        "VALUE": "0",
        "UNIT": "m",
        "STATEMENT": "only motion on the spring axis is described: z = 0"
      }
    ],
    "BOUNDARY": [
      {
        "NAME": "B_small",
        "PREDICATE": "|x| < x_max",
        "REFS": ["x", "x_max"],
        "CONDITION": "x / x_max < 1"
      }
    ]
  },
  "TrM": {
    "HEADER": {
      "ENVIRONMENT_INVENTORY": [
        {"ENVIRONMENT_QUANTITY": "time", "DIMENSION": "T1"},
        {"ENVIRONMENT_QUANTITY": "position", "DIMENSION": "L1"},
        {"ENVIRONMENT_QUANTITY": "velocity", "DIMENSION": "L1 T-1"},
        {"ENVIRONMENT_QUANTITY": "transverse_position", "DIMENSION": "L1"}
      ],
      "SIGNATURE": [
        {
          "NAME": "time_derivative",
          "OVER": ["x", "v", "t"],
          "IMAGE": "d/dt maps position to velocity",
          "FORM": "D(x, t) = v",
          "IMAGE_FORM": "D(position, time) = velocity"
        }
      ],
      "TRANSFORMATIONS": [
        {"NAME": "time_translation", "STATEMENT": "t -> t + t0"}
      ]
    },
    "ENTRIES": [
      {
        "NAME": "E_t",
        "DOF": "t",
        "DOMAIN": "always",
        "ENVIRONMENT_QUANTITY": "time",
        "IDENTIFICATION": "t is the reading of a laboratory clock from an arbitrary origin",
        "FALSIFIER": "a second clock whose readings differ from t by more than a constant offset beyond the stated uncertainty",
        "FALSIFIER_CLASS": "F3",
        "BEARS": [],
        "DIMENSION": "T1"
      },
      {
        "NAME": "E_x",
        "DOF": "x",
        "DOMAIN": "|x| < x_max",
        "ENVIRONMENT_QUANTITY": "position",
        "IDENTIFICATION": "x is the displacement of the mass along the spring axis from the point where the spring exerts no force",
        "FALSIFIER": "a measured spring force not proportional to x inside the domain",
        "FALSIFIER_CLASS": "F3",
        "BEARS": ["EOM_X", "KIN"],
        "DIMENSION": "L1"
      },
      {
        "NAME": "E_v",
        "DOF": "v",
        "DOMAIN": "|x| < x_max",
        "ENVIRONMENT_QUANTITY": "velocity",
        "IDENTIFICATION": "v is the rate of change of x with t",
        "FALSIFIER": "a measured velocity that differs from the rate of change of the measured x beyond uncertainty",
        "FALSIFIER_CLASS": "F2",
        "BEARS": ["KIN"],
        "DIMENSION": "L1 T-1"
      },
      {
        "NAME": "E_z",
        "DOF": "z",
        "DOMAIN": "always",
        "ENVIRONMENT_QUANTITY": "transverse_position",
        "IDENTIFICATION": "z is the displacement of the mass perpendicular to the spring axis",
        "FALSIFIER": "a measured z different from 0 beyond its uncertainty",
        "FALSIFIER_CLASS": "F3",
        "BEARS": ["EOM_Z", "C_NOZ"],
        "DIMENSION": "L1"
      }
    ]
  },
  "TMS": {
    "PARAMETERS": {
      "STEP_CONVENTION": "one application of an inference rule or algebraic identity is one step",
      "K": "2",
      "N_X": 2,
      "S_MAX": 10
    },
    "CONSTANTS": [
      {"NAME": "w_a", "VALUE": "1"},
      {"NAME": "w_s", "VALUE": "0.5"}
    ],
    "YARDSTICKS": [
      {
        "NAME": "combined_distance",
        "KEY": ["SR1", "WSUM:w_a*A;w_s*S", "S"],
        "LIMITING": []
      }
    ]
  }
}