What Physics Engines Solve

A physics engine simulates how rigid bodies move and interact:

• Gravity pulls objects down.
• Forces apply.
• Bodies collide and bounce.
• Friction slows motion.

Used in:

• Games: realistic ball bouncing, character collision, vehicle physics.
• Simulations: engineering, training (driving sim, robotic arms).
• Animation: ragdolls, cloth, fluids.
• Scientific: molecular dynamics, astrophysics.

Real engines:

• Box2D (Erin Catto): 2D, used in Angry Birds.
• Bullet Physics: 3D, used in many games + films.
• PhysX (NVIDIA): GPU-accelerated 3D.
• Havok: commercial AAA.
• Chipmunk: 2D, simpler than Box2D.
• Rapier (Rust): modern, fast.

We'll build 2D rigid body physics. Includes:

• Vector math.
• Numerical integration (Euler, Verlet).
• AABB / circle collision detection.
• Impulse-based response.
• Constraints (joints).
• Broad-phase optimization.

By the end: balls bouncing in a box, stacked boxes, characters jumping.

Reference: Game Physics Engine Development (Millington), Box2D source, Erin Catto's GDC talks.

Each frame:

1. Integrate forces → velocities → positions.
2. Detect collisions.
3. Resolve collisions (impulses).
4. Render.

Loop runs at fixed step (e.g., 60 Hz). Frame time independent.

Modern games use physics for everything from cloth in characters' clothing to destructible environments. Physics is a core engine subsystem.