Add realistic heavy-symmetric-top dynamics on the nutation screen

[veillette]

Screen 1 models a top with the idealized Ω = τ/(Iω) relation, which assumes
the axis is handed exactly the steady-precession rate and holds its tilt
forever. Screen 2 now integrates the same apparatus from its full Lagrangian
instead, so the tilt is a dynamical variable and a released top behaves like a
real one: the axis dips, picks up precession, rises again, and its tip traces
cusps, loops, or smooth waves depending only on how it was released.

Physics (src/common/rigid-body/HeavySymmetricTopPhysics.ts):

• Euler-angle equations of motion for a heavy symmetric top, integrated with
  RK4 at a 0.5 ms internal substep
• Turning points from the effective potential, by bisecting the cubic in cos θ
• Steady-precession roots and the critical spin below which no steady solution
  exists, plus the sleeping-top stability criterion
• Optional viscous friction (drag on the center of mass, spin friction at the
  pivot) that damps the nutation and spins the top down until it falls
• Inelastic mechanical stop where the axle rests against its mount

Screen:

• Perspective view of the wheel with the tip path and the two dashed circles
  bounding the nutation band, drawn via an exact linear projection of the
  Euler frame (src/common/view/TopProjection.ts)
• θ(t) graph with the turning points as reference lines
• Controls for spin, release tilt, release mode, and friction, with readouts
  for the band, both frequencies, and the critical spin
• Slow-motion option, since nutation and precession differ by roughly 5× in rate
• Live accessible summary and localized strings in en/fr/es

Apparatus constants are a demonstration gyroscope wheel: ω_nut · Ω_slow =
M g l / I₁ is fixed by the apparatus alone, so the wheel is deliberately large
and short-armed to bring both timescales on screen at once.

Tests assert the integrator against analytic results — energy and both angular
momenta conserved to 6+ decimals over 10 s, exact steady precession at the
fixed point, motion confined to and reaching the predicted turning points, and
the fast-top nutation frequency I₃ω₃/I₁.

Also moves PlayAreaPanel to src/common/view so both screens can use it.

Co-Authored-By: Claude Opus 5 noreply@anthropic.com
Claude-Session: https://claude.ai/code/session_01H6aawcC32DhbbRsgmeugbk

[cursor]

Bugbot is not enabled for your account, so this pull request was not reviewed.

Enable Bugbot in the Cursor dashboard to get automatic reviews on future PRs.