Overview
Rigid Body Dynamics tracks linear and angular motion, applies forces and torques, and resolves contacts or constraints between bodies.
CoreSource checked
Rigid Body Dynamics
Simulates objects that translate and rotate while keeping their shape fixed.
Quick Facts
Compact metadata for implementation and discovery.
- Category
- Simulation
- Difficulty
- Advanced
- Family
- Physics Simulation
- Tier
- Core
- Status
- Verified
- Review
- Source Checked
- Sources
- 1
- Formulas
- 1
- Relationships
- 3
- Code example
- Ready
- Visualization
- Ready
Core Concepts
linear momentumangular momentumcontact impulseinertia tensor
Quick facts
Complexity
Runtime and memory behavior at a glance.
Best
O(bodies)
Average
O(bodies + contacts)
Worst
O(bodies + contacts^3)
Space
O(bodies + contacts)
When to Use
- Use when objects should move and collide without deforming.
- Use when game physics is a central requirement.
When Not to Use
- Avoid when deformation, fluid flow, or soft-body behavior is the primary effect.
- Avoid when the timestep, constraints, or stability requirements exceed what the method can handle.
What It Does
- Computes physics simulation within Physics Simulation workloads (O(bodies + contacts) time, O(bodies + contacts) space).
- Works by Simulates objects that translate and rotate while keeping their shape fixed.
- Maintains key invariants across linear momentum, angular momentum, contact impulse.
Use Cases
- Game physics
- Robotics simulation
- Mechanical prototyping
Inputs
- Rigid bodies
- Mass and inertia
- Forces
- Contacts
Outputs
- Updated positions
- Updated velocities
- Contact impulses
Key Formulas (1)
Linear acceleration
acceleration = force / mass
acceleration = force / massUpdates translational motion from accumulated forces.
Pseudocode
- 1.Accumulate forces and torques
- 2.Integrate velocities
- 3.Detect collisions
- 4.Solve contact constraints
- 5.Integrate positions and orientations
Canonical Example
- Input
- box falls onto floor
- Output
- box position stops at contact and velocity changes
- Explanation
- Collision impulses prevent penetration and adjust motion.
Implementation Notes
- Represent orientation with quaternions or rotation matrices and normalize when needed.
- Keep units, timestep size, and state variables explicit in tests.
- Keep a tiny example with expected output beside the implementation.
Common Pitfalls
- Using center-of-mass forces for contact impulses ignores rotation.
- Large timesteps can add energy, damp motion, or make constraints explode.
- Not defining boundary, empty, or degenerate inputs before implementation.
Interactive Mechanism Walkthrough
Iterative Convergence & State TrajectoryShow boxes moving, rotating, and receiving impulses at contact points.
Step 1 of 5: Accumulate forces and torques
simulation-stateNotes
Stable contacts and stacking require careful constraint solving.
Sources (1)
What each reference supports for this entry.
Physically Based Modeling
DocumentationSIGGRAPH course notes covering integration, particles, constraints, and rigid-body simulation.
Open sourceExplore Next
Good next jumps from the relationship graph, ranked for useful discovery.
Relationships
View full relationship pageRigid-body simulation pipelines use broad phase to find possible contacts.
Often paired withSequential Impulse Solver
Rigid-body engines often use sequential impulses for contacts and joints.
Related Algorithms
Tags
SimulationPhysicsRigid BodyCollision Detection