File size: 3,852 Bytes
b99b9ee | 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 | """Tier-2 physical systems: damped or with a second active force term."""
from __future__ import annotations
import numpy as np
from physix.systems.base import PhysicalSystem, SystemTier
class DampedPendulum(PhysicalSystem):
"""Pendulum with linear angular damping.
Equation of motion: ``d2theta/dt2 = -(g/L)*sin(theta) - b*dtheta``.
"""
system_id: str = "damped_pendulum"
tier: SystemTier = SystemTier.TIER_2
state_variables: tuple[str, ...] = ("theta", "dtheta")
hint_template: str = (
"Pendulum of length {L:.2f} m. Oscillation amplitude visibly decreases "
"over time, suggesting linear angular damping."
)
def sample_parameters(self, rng: np.random.Generator) -> dict[str, float]:
return {
"g": 9.81,
"L": float(rng.uniform(0.5, 2.0)),
"b": float(rng.uniform(0.05, 0.30)),
}
def sample_initial_conditions(self, rng: np.random.Generator) -> dict[str, float]:
return {
"theta": float(rng.uniform(0.3, 1.0)),
"dtheta": 0.0,
}
def rhs(
self,
t: float,
state: np.ndarray,
params: dict[str, float],
) -> np.ndarray:
theta, dtheta = state
d2theta = -(params["g"] / params["L"]) * np.sin(theta) - params["b"] * dtheta
return np.array([dtheta, d2theta], dtype=float)
def ground_truth_equation(self) -> str:
return "d2theta/dt2 = -(g/L)*sin(theta) - b*dtheta"
class SpringMass(PhysicalSystem):
"""Undamped harmonic oscillator.
Equation of motion: ``d2x/dt2 = -(k/m) * x``.
"""
system_id: str = "spring_mass"
tier: SystemTier = SystemTier.TIER_2
state_variables: tuple[str, ...] = ("x", "vx")
hint_template: str = (
"Mass {m:.2f} kg attached to a spring of stiffness {k:.2f} N/m, "
"frictionless surface."
)
def sample_parameters(self, rng: np.random.Generator) -> dict[str, float]:
return {
"k": float(rng.uniform(2.0, 20.0)),
"m": float(rng.uniform(0.5, 2.0)),
}
def sample_initial_conditions(self, rng: np.random.Generator) -> dict[str, float]:
return {
"x": float(rng.uniform(0.5, 2.0)),
"vx": 0.0,
}
def rhs(
self,
t: float,
state: np.ndarray,
params: dict[str, float],
) -> np.ndarray:
x, vx = state
return np.array([vx, -(params["k"] / params["m"]) * x], dtype=float)
def ground_truth_equation(self) -> str:
return "d2x/dt2 = -(k/m) * x"
class DampedSpring(PhysicalSystem):
"""Damped harmonic oscillator.
Equation of motion: ``d2x/dt2 = -(k/m)*x - (c/m)*vx``.
"""
system_id: str = "damped_spring"
tier: SystemTier = SystemTier.TIER_2
state_variables: tuple[str, ...] = ("x", "vx")
hint_template: str = (
"Mass {m:.2f} kg on a spring of stiffness {k:.2f} N/m with viscous "
"damping coefficient {c:.2f}. Oscillation amplitude decays over time."
)
def sample_parameters(self, rng: np.random.Generator) -> dict[str, float]:
return {
"k": float(rng.uniform(2.0, 20.0)),
"m": float(rng.uniform(0.5, 2.0)),
"c": float(rng.uniform(0.1, 1.0)),
}
def sample_initial_conditions(self, rng: np.random.Generator) -> dict[str, float]:
return {
"x": float(rng.uniform(0.5, 2.0)),
"vx": 0.0,
}
def rhs(
self,
t: float,
state: np.ndarray,
params: dict[str, float],
) -> np.ndarray:
x, vx = state
d2x = -(params["k"] / params["m"]) * x - (params["c"] / params["m"]) * vx
return np.array([vx, d2x], dtype=float)
def ground_truth_equation(self) -> str:
return "d2x/dt2 = -(k/m)*x - (c/m)*vx"
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