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Sequential Impulse Solver

Approximates rigid-body contact and joint constraints by applying clamped impulses one constraint at a time.

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Quick Facts

Compact metadata for implementation and discovery.

Category: Simulation
Difficulty: Advanced
Family: Constraint Solver
Tier: Core
Status: Verified
Review: Source Checked
Sources: 1
Formulas: 1
Relationships: 4
Code example: Ready
Visualization: Ready

Overview

A sequential impulse solver iterates over contacts and joints, computes an impulse from relative velocity and effective mass, clamps it to normal or friction limits, and immediately applies it to the connected bodies.

Core Concepts

velocity constrainteffective massimpulse clampingwarm startingiterative solvercontact constraint

Quick facts

Complexity

Runtime and memory behavior at a glance.

Best

O(constraints)

Average

O(iterations * constraints)

Worst

O(iterations * constraints)

Space

O(constraints)

When to Use

Use when real-time performance matters more than exact global constraint solves.
Use when contacts and joints can be resolved over several iterative passes per timestep.

When Not to Use

Avoid when high-precision offline dynamics or exact constraint satisfaction is required.
Avoid when extreme mass ratios, stiff stacks, or large timesteps dominate without extra stabilization.

What It Does

Computes constraint solver within Constraint Solver workloads (O(iterations * constraints) time, O(constraints) space).
Works by Approximates rigid-body contact and joint constraints by applying clamped impulses one constraint at a time.
Maintains key invariants across velocity constraint, effective mass, impulse clamping.

Use Cases

Interactive rigid-body physics where fast approximate contact resolution is acceptable.
Games and simulations with many contacts, joints, or friction constraints.
Physics demos that need stable-enough behavior at fixed timestep budgets.

Inputs

Current state
Forces or constraints
Time step

Outputs

Updated state
Constraint corrections
Collision results

Key Formulas (1)

Normal impulse update

δ_j = −(J·v + bias) / (J·M⁻¹·J^T)

delta_j = -(J*v + bias) / (J*M^-1*J^T)

Computes a corrective impulse increment from constraint velocity error, bias, and effective mass before clamping.

Pseudocode

1.Build contact and joint constraints for the current timestep
2.Warm start by applying cached impulses for persistent contacts
3.Repeat for the configured solver iteration count
4.For each constraint, compute relative velocity and bias error
5.Compute impulse delta from effective mass
6.Clamp accumulated impulse to the constraint limits
7.Apply the impulse delta to the connected bodies

Canonical Example

Input: a dynamic box moving downward into a static floor contact
Output: a clamped upward normal impulse reduces the closing velocity at the contact
Explanation: The solver updates the box velocity immediately so the contact constraint is closer to non-penetrating.

Implementation Notes

Build each constraint with Jacobian direction, effective mass, bias, and impulse limits.
Apply normal and friction impulses with separate clamping rules.
Run several iterations and keep timestep size stable when comparing behavior.

Common Pitfalls

Forgetting accumulated impulse clamping can make contacts attract or jitter.
Warm-start impulses must correspond to the same persistent contact points.
Solver order, timestep, iteration count, and friction model all affect convergence.