Mathematical Foundations

This section of the Wiki focuses on the mathematical theory, derivations, and reformulations that guide the structure and functionality of the physics engine.

The goal is to derive each model from first principles and restructure it in a form suitable for numerical simulation—especially matrix-based computation optimized for GPU acceleration.

Although implementation is still in early stages, this section will document the full theoretical development as it evolves.

Topics

The following categories will eventually contain detailed derivations and explanations:

1. Newtonian Mechanics (Classical Foundation)

• Translating classical equations of motion into matrix form
• Rigid body dynamics and constraint modeling

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More to be announced

Status

The mathematics behind this project is currently in development. As derivations are completed and validated, they will be documented here with references, diagrams, and commentary.

Each page will aim to:

• Derive the concept from first principles
• Show how it can be expressed in matrix form
• Discuss numerical and computational considerations
• Link directly to corresponding code (when available)

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