feat(ClassicalMechanics): pendulum trajectories on the configuration circle and the bridge to physical space

[aadarwal]

Toward #883 — closes the tracker's trajectory and Lagrangian requirements: with this PR the parent
pendulum API map has no N/A rows left.

Stacked. Base is the Hamiltonian PR #1570 (branch pendulum/pr3-hamiltonian, bda52edb).
The commits belonging to this PR are the last two (865163fb, f113b6bb), touching two new
modules, Physlib.lean, and both API maps. Please review after #1570.

Two new modules under SimplePendulum/Geometric/:

Trajectory.lean — Trajectory := Time → ConfigurationSpace; Trajectory.ofLift (the
trajectory described by a lift of the angle) with: invariance under whole-turn shifts
(ofLift_add_int_mul_two_pi), ofLift_eq_iff (two lifts give the same trajectory iff at each
time they differ by whole turns — the quantifiers are ∀ t, ∃ n; the uniform-n version is
false), continuity, and contMDiff_ofLift (a C^n lift describes a C^n curve in the circle —
forward direction only; the converse needs the covering-map lift and is deferred honestly); the
bob's position along a trajectory with the rod-length constraint.

PhysicalSpace.lean — spaceTrajectory (the bob's position for a fixed pendulum), its
velocity (ℓ cos θ, ℓ sin θ)·θ̇ and speed ℓ²θ̇², and the payoff identities under
Differentiable ℝ θ: kineticEnergy_eq_space (½ I θ̇² = ½ m ‖v‖²), potentialEnergy_eq_height
(V = m g h, h from the bottom of the swing), lagrangian_eq_space — the chart Lagrangian of
#1564 is the constrained Lagrangian of a point mass on the circle of radius ℓ — and
energy_eq_space.

deriv_sin_coord/deriv_cos_coord are general chain-rule facts kept local to keep this PR to one
file pair; happy to promote them to Time/Derivatives.lean in a follow-up if preferred.

Reviewer reading order: Trajectory.lean §A (check ofLift_eq_iff's quantifiers), §B, §C;
then PhysicalSpace.lean §A–B (the global-Differentiable hypothesis comes from the Time.deriv
API), §C (the four identities); the API maps last — the parent's trajectory and Lagrangian rows
flip to done, the Lagrangian row citing both the definition (SimplePendulum.lagrangian,
Basic.lean) and the identification proved here.

Verification: full lake build + complete linter battery pass; axiom audit clean; the two new
modules' imports verified minimal.

Developed with assistance from AI; all mathematics and proofs were reviewed and verified to compile.

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