Migrated from Method backlog

This issue was created from a legacy filesystem backlog card. GitHub Issues are now the live work tracker; repository docs remain Method evidence.

Source backlog: docs/method/backlog/cool-ideas/MATH_tumble-tower-stage-1-rotation.md
Original lane: cool-ideas
Original legend: MATH

Original backlog card

Milestone: Tumble Tower | Priority: P2

Status: active cool idea. Task DAG issue #232 is still open and blocked by
Stage 0 (#231). F32Scalar::sin_cos and trig golden-vector tests exist, but
no Tumble Tower OBB, angular dynamics, contact manifold, or torque solver
exists yet.

Stage 1: Rotation

Issue: #232

User Story: As a learner progressing through the physics ladder, I want rotation and oriented bounding boxes so that I can see how angular dynamics and OBB contact detection work deterministically.

Requirements

• R1: Extend body representation with rotation angle (radians, stored as F32Scalar) and angular velocity.
• R2: Implement OBB-vs-OBB overlap detection using separating axis theorem (4 axes for 2D).
• R3: Implement contact point computation for OBB pairs (edge-vertex and edge-edge cases).
• R4: Apply torque from off-center contact forces (moment arm x contact impulse).
• R5: All trigonometric operations use F32Scalar::{sin, cos, sin_cos} backed
  by the deterministic LUT trig implementation; do not call platform
  f32::{sin, cos} in authoritative simulation code.

Acceptance Criteria

• AC1: A rotated box (30 degrees) dropped onto a flat surface produces a deterministic rotation sequence.
• AC2: Two rotated boxes collide and exchange angular momentum correctly.
• AC3: Golden vector: specific rotated-stack scenario matches known fingerprint.
• AC4: Cross-OS test: same scenario on macOS and Linux produces identical fingerprints (deterministic trig verification).

Definition of Done

• Code reviewed and merged
• Tests pass (CI green)
• Documentation updated (if applicable)

Scope: Rotation, angular velocity, OBB SAT, contact points, torque.
Out of Scope: Friction/restitution (Stage 2); sleeping (Stage 3); continuous collision detection.

Test Plan

• Goldens: Golden fingerprint for a 3-OBB collision scenario over 100 ticks.
• Failures: Degenerate OBB (zero-width, handled as line segment); angular velocity exceeding one full rotation per tick (clamped).
• Edges: Boxes at exactly 0/90/180/270 degrees (axis-aligned OBB should match AABB results); two boxes with identical rotation and position (perfect overlap).
• Fuzz/Stress: Property test: random rotations and positions for 8 OBBs, verify SAT returns the same result as a brute-force overlap check.

Blocked By: stage-0-aabb
Blocking: stage-2-friction

Est. Hours: 6h
Expected Complexity: ~500 LoC