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The science
The model: a pressurised mesh of springs
The jelly skin is an icosphere of N point masses m = M/N joined by damped Hooke springs, F = k (L − L0) + c (dL/dt) along each edge. Inside is a fixed amount of gas at constant temperature, so p = nRT / V. The enclosed volume comes from the divergence theorem, V = (1/6) Σ ra · (rb × rc) over the outward triangles, and the gas pushes each face with force p · S (S = face area vector), shared equally by its three corners. Time stepping is semi-implicit Euler at 1/2000 s.
Why the gas matters
Squeezing shrinks V and raises p, so the gas acts as a soft nonlinear spring on the volume (free energy −nRT ln(V/V0)). A free body settles where skin tension balances pressure. For a body in equilibrium with no external load, the virial theorem links the elastic forces to the gas: Σ ri · Fispring + 3pV = 0, which the page evaluates live and in a separate check. A leak lowers nRT until gravity flattens the body.
Contact and press
Nodes that pass through the floor, ramp, obstacle ball or press plate are projected back to the surface; the normal velocity is reversed by restitution e and tangential velocity is limited by Coulomb friction |Jt| ≤ μ Jn. The press force is the impulse removed from the nodes per unit time; for a slow squeeze it approaches p × contact area.
Honest simplifications
Only the skin carries stiffness (no bulk shear waves), the gas is isothermal rather than adiabatic during fast impacts, and the mesh cannot tear. It is an educational model of a pressurised soft body, not a finite-element jelly.
Model checks in this page
(1) the virial identity for a free relaxed body; (2) free fall of the centre of mass y = y0 − g t2/2; (3) the time-averaged floor reaction of a resting body equals its weight m g.