Eternal Energy Simulation — Conservation vs. Dissipation

IDEAL — ENERGY CONSERVED

Dissipation

Damping γ 0.00 /s

System

Gravity g 9.8 m/s²

Rod length L 1.6 m

Live Readouts

Kinetic E

0.000 J

Potential E

0.000 J

Total Energy

0.000 J

Entropy ΔS

0.000 mJ/K

How it works

The bob is a spherical pendulum: a mass on a rigid rod of length L, free to swing in any direction under gravity, described by a polar angle θ (from straight down) and azimuth φ. Its Lagrangian gives the exact equations of motion:

θ'' = φ'² sinθ cosθ − (g/L) sinθ − γθ'
φ'' = −2θ'φ' cosθ/sinθ − γφ'

KE = ½mL²(θ'² + sin²θ·φ'²)
PE = mgL(1 − cosθ)
E_total = KE + PE

With γ = 0 (Ideal / "eternal" mode) no term removes energy from the system: E_total oscillates only from numerical rounding and stays flat over time — a working model of a closed system where energy is neither created nor destroyed, exactly as the first law of thermodynamics requires.

With γ > 0, a velocity-proportional drag term removes mechanical energy at rate P = 2γ·KE. That energy doesn't vanish — the second law says it must reappear as heat in the surroundings. Assuming an environment at T = 300 K, the entropy generated is tracked as:

dS/dt = P / T_env   (Clausius: entropy produced by irreversible heat release)

The bob's color shifts from cool blue toward hot orange with its instantaneous kinetic energy, and the trailing path fades — a visual stand-in for the "arrow of time" that a damped, real system always has and a perfectly ideal one never does.

Damping γ — 0 keeps the system ideal/lossless; higher values drain energy faster into heat.
Gravity / Rod length — change the pendulum's natural frequency and the shape of its conical/chaotic swing.
Kick — injects a burst of angular velocity, a clean way to see how added energy is conserved (γ=0) or bleeds away (γ>0).

Rod & pivot Bob (cool → hot by KE)

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