DART Background Theory

Theoretical background materials derived from academic publications by DART's original authors.

Note: These documents explain the mathematical foundations. For code-level exploration, see docs/onboarding/. For boundaries between theory background, design rationale, plans, and published docs, use docs/information-architecture.md.

Attribution

The materials in this section are derived from:

Document	Authors	Original	Status
Multibody Dynamics Tutorial	C. Karen Liu, Sumit Jain	docs/dynamics.pdf	Migration in progress
LCP Contact Handling	Jie Tan, Kristin Siu, C. Karen Liu	docs/lcp.pdf	✅ Migrated

These documents were reformatted from PDF to Markdown for maintainability while preserving the original authors' work. The original PDFs remain in the repository as authoritative references.

For the full attribution template, see ATTRIBUTION.md.

Contents

Use this file as the theory entrypoint. Add new research-foundation topics as peer sections here, then point to topic-specific directories or pages below.

Dynamics

Lagrangian dynamics for articulated rigid body systems:

1. Introduction — Prerequisites and scope
2. Lagrangian Dynamics — D'Alembert's principle, virtual work
3. Newton-Euler Review — Single rigid body dynamics
4. Rigid Body Lagrange — Lagrange's equations for rigid bodies
5. Articulated Dynamics — Equations of motion: M(q)q̈ + C(q,q̇) = Q
6. Coordinate Conversion — Cartesian ↔ generalized coordinates
7. Recursive Inverse Dynamics — Efficient O(n) algorithms

Notation Glossary: dynamics/notation-glossary.md

LCP Solvers

Contact handling via Linear Complementarity Problems:

1. Problem Statement — LCP definition, DART convention (w = Ax - b)
2. Overview — Solver taxonomy and comparison
3. Pivoting Methods — Dantzig, Lemke algorithms
4. Projection Methods — PGS, Jacobi, iterative solvers
5. Newton Methods — Smooth reformulations
6. Other Methods — Interior point, QP-based
7. Selection Guide — Which solver to use when

Related Documentation

Topic	Location	Description
Dynamics code exploration	docs/onboarding/dynamics.md	API walkthrough
Constraint system	docs/onboarding/constraints.md	Solver internals
Control theory	docs/readthedocs/topics/control-theory.md	Notation mapping
DART 7 references	docs/readthedocs/papers.md	Research paper/textbook/engine catalog for the DART 7 simulation world (status, priority, verdict)

For AI Agents

See AGENTS.md for guidelines on working with these documents.