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Presets
Parameters
Model checks
The science
What is modelled
Two balls of mass m hang on arms of length L = 0.81 m pivoted 0.15 m off the spindle; links of 0.75 m connect them to a sleeve of mass M that slides on the spindle. In the rotating frame the system has the effective potential below.
Equations
Ueff(θ) = 2 m g z_b − m ω² r² + M g z_s with r = X0 + L sin θ, z_b = H − L cos θ, z_s = z_b − √(B² − (r − S)²). Equilibrium: dUeff/dθ = 0. Dynamics: I(θ) θ̈ = −dUeff/dθ − ½ I′ θ̇² − c θ̇. Ideal limit: cos θ = g/(ω² L).
Honest simplifications
Frictionless pivots except the lumped viscous term c, massless links, a fixed spindle speed in open-loop mode, and a simple linear valve and engine model in closed-loop mode (illustrative torques). The 3D page uses a fitted angle curve; this page solves the force balance, so the numbers differ.
Built-in checks
The ideal conical-pendulum limit, a stationarity and stability test of the potential, and the small-oscillation period against 2π√(I/U″).