Rigid-body physics

Each body holds mass, an inertia tensor, position, orientation, and linear and angular velocity. Each step the engine applies forces and gravity, finds colliding pairs with a broad phase and contact points with a narrow phase, solves contact and joint constraints iteratively (sequential impulses or projected Gauss-Seidel), and integrates positions; resting bodies sleep to save compute. Engines include Havok, used for Half-Life 2's gravity gun puzzles in 2004, PhysX, and Box2D by Erin Catto. Dennis Gustafsson's voxel physics engine after Teardown uses substeps instead of more solver iterations, in the style of temporal Gauss-Seidel, with a parallel solver for large piles. Outputs are motion, contact events, and impact forces that other systems read as damage or sound.

Tactile and playful. Objects behave as expected, so players stack, throw, and build contraptions, and failures turn into slapstick. Physics puzzles feel solved by understanding rather than by finding the intended key.

• solver iterations or substeps per frame
• friction and restitution per material
• allowed mass ratios between interacting bodies
• joint types and limits
• sleep thresholds and active simulation range
• determinism requirements for replays and networking

• Large mass ratios and stiff joints cause jitter or explosive separation.
• Fast small objects tunnel through thin walls without continuous collision detection.
• Non-deterministic solvers desynchronize multiplayer sessions and replays.
• Players exploit clipping and stacking to launch themselves or bypass level geometry.
• Body count caps scale and causes late slowdowns in sandbox play.

• Contraptions, chain reactions, and Rube Goldberg machines arise in sandboxes such as Garry's Mod, whose tool gun welds and constrains props.
• Impact forces feed damage, sound, and destruction systems.
• Ragdoll physics turns failure into comedy and shareable clips.

• Can learned simulators handle thousands of interacting bodies more cheaply than iterative solvers while staying stable?
• Can deterministic GPU solvers make large rigid-body worlds practical in multiplayer?