Quick Physics Tutorial

Physics Simulation Without the Headache

Most people approaching physics for games, VFX, or prototyping end up spinning their wheels because they skip the boring parts. They want to build something that moves and collides without understanding why things explode mid-simulation. This guide cuts through that. You'll get practical steps, not fluff. A proper physics tutorial assumes you already know basic vector math—dot products, cross products, normalization, and how to represent a 3×3 rotation matrix. If you don't, spend two days on linear algebra first. You'll save hours later. The alternative is copying code you can't debug when it breaks. I've watched juniors try to skip that foundation. One guy spent three weeks debugging a rolling sphere that kept flying off at 400 m/s. The issue was a single NaN propagating through the quaternion integration. His solver wasn't broken. His math was. He hadn't normalized his quaternion in 14 frames. Now he checks normalization on every step and hasn't looked back.

Choosing the Right Approach

Physics engines generally fall into two camps: impulse-based solvers and constraint-based solvers. Impulse methods are faster but struggle with stacking stability. Constraint methods like sequential impulse or LCP (Linear Complementarity Problem) solvers handle stacks well but eat CPU cycles. Most hobby projects pick impulse-only and then complain about jitter. That's a choice, not a bug. If you're doing Quick Physics Tutorial material or starting out, begin with a basic impulse solver. Get one rigid body falling. Then add collision detection. Then add a second body. Each step adds complexity exponentially. Do not jump ahead.

Collision Detection: The Part Everyone Rushes

Broad phase first. Use a sweep-and-prune or spatial partition like an AABB tree. GJK/EPA only comes after you've narrowed it down to a candidate pair. I learned this the hard way when a prototype tried running GJK against every object on every frame with 800 entities. It ran at 3 FPS on a desktop machine. For continuous collision detection (CCD), most engines use swept spheres or capsule tests. Full poly-to-poly CCD is computationally expensive and rarely worth it unless you're simulating high-velocity projectiles. A swept sphere test catches 95% of tunneling cases for a fraction of the cost.

Integrating Motion

Verlet integration is stable for constraints but feels wrong for angular motion. Semi-implicit Euler is cheap and stable enough for simple games. Runge-Kutta 4 is overkill unless you're doing something like orbital mechanics where energy conservation matters across thousands of steps. For angular dynamics, work with quaternions, not Euler angles. I repeat: not Euler angles. Gimbal lock will visit you. It always does. When you do use quaternions, re-normalize every frame or every few frames. Drift accumulates faster than you'd think.

My Favorite Workaround for the Rotation Drift Problem

I worked on a rigging tool once where the physics layer used quaternions and the artist tools used Euler angles. The bridge between them caused a specific edge case: when the roll angle hit exactly ±90°, the quaternion would snap to a conjugate state that looked correct but behaved backwards under subsequent rotations. No error message. Just silent nonsense. The fix was to detect when the quaternion's scalar component crossed zero during interpolation and flip all four components simultaneously to maintain continuity. Simple, but I didn't find it in any textbook. I found it by watching a character's arm twist itself inside out during a blend animation.

Constraints and Joints

Positional constraints correct velocity errors after the fact. Angular constraints work the same way but need axis-angle representation. The key insight nobody emphasizes enough: constraint stiffness is not free. A stiff constraint requires smaller time steps or iterative solving. Soft constraints are cheaper but look squishy. Most tutorials show a simple hinge joint. Real projects need spring-damper systems for suspension, soft-body constraints for clothing, and motorized joints for animatronics. Each adds parameters you need to tune. A suspension system with a spring constant of 5000 N/m and damping of 500 Ns/m looks nothing like one with 2000 and 200. There's no universal right answer.

Common Pitfall: Stacking Instability

A stack of 20 boxes will fall apart regardless of which solver you use unless you enable position correction. Velocity correction alone creates micro-bouncing that compounds over frames. Position correction pushes overlapping bodies apart after the velocity step. The combined approach—solver then projector—is what keeps stacks stable. Even with both, very tall stacks (30+ bodies) will still destabilize. The workaround is to merge static-adjacent boxes into compound shapes or convex hulls. Three stacked boxes become one object. Stability improves dramatically because you've removed 24 contact points from the simulation.

Tuning and Debugging

Write a debug visualizer early. Position, velocity, contact normals, and impulse magnitude as colored lines. When something breaks, you should see it immediately. I've lost entire days chasing bugs that a single debug render would have revealed in seconds. Log your simulation state to CSV periodically. Time step, object positions, energies. Plot kinetic versus potential energy. If total energy isn't conserved (for a closed system), you know your integrator is leaking. That leak tells you where to look.

When Physics Simulation Isn't the Answer

Here's the honest part: for many projects, you don't need a physics engine. Animation curves, particle systems, and pre-baked simulation data are often better. A swinging door? Keyframe it. Rubbing leaves? Particle emitter. Cloth on a character? Use a skinning modifier or pre-simulated cache. Physics simulation introduces uncertainty. You cannot predict exact outcomes frame-by-frame without deterministic locking, and even then floating-point variance across platforms causes drift. If your project demands frame-perfect reproducibility—speedrunning tools, networked gameplay with lockstep netcode—you either constrain the simulation heavily or accept occasional desync.

The Quick Physics Tutorial You Should Actually Read

If you're looking for a structured Quick Physics Tutorial, start with Erin Catto's GDC talks on Box2D. They're not flashy but they explain why the engine works the way it does. Then move to Miller's Game Physics Engine Development if you want to build one yourself. Skip the textbooks that only derive equations without showing code. There's a reason most indie physics implementations fail. Not because the math is hard. Because the edge cases are invisible until your game is shipped. Stack overflow, tunneling, floating-point drift, constraint coupling—that's where the real work lives. Learn those first. Everything else is documentation.