Math‐Newtonian - StevenKight/Physics-Engine GitHub Wiki
Newtonian Physics in Matrix Form
This section provides a general overview of how Newtonian mechanics is approached within the High-Performance Physics Engine. The goal is to establish a classical foundation using Newton’s laws, from which modern formulations (e.g., Lagrangian, Hamiltonian, or geometric mechanics) may later evolve or replace specific components.
Purpose of This Section
- Provide a clear, structured formulation of Newtonian mechanics using matrix operations.
- Lay the groundwork for GPU-accelerated simulation using CUDA and cuBLAS.
- Offer a reference framework for testing, benchmarking, and validating alternative models in the future.
Approach
This project reformulates classical Newtonian physics with an emphasis on:
- Vector and matrix representations of force, velocity, and acceleration
- Numerical integration schemes compatible with GPU computation
- System-wide representations of multi-body dynamics and constraints
While classical Newtonian physics is scalar in its original form, this project aims to express all relationships using linear algebra, enabling high-throughput computation on modern hardware.
Guiding Principles
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Start simple, scale later
Begin with basic particle systems and rigid body mechanics, with progressively more complexity introduced. -
Matrix-first design
All physics equations are recast into matrix form early in the derivation to facilitate GPU acceleration. -
Modularity of physics
Forces, constraints, and integration steps are designed to be swappable. For example, Newtonian dynamics can later be replaced with Lagrangian dynamics without restructuring the rest of the engine. -
Numerical stability as a priority
Emphasis is placed on stability under high-performance simulation, especially when using lower-precision GPU floats.
Topics Covered
Each of these topics will be elaborated on in separate sub-pages with full derivations and examples.
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