Volume 0: The Mathematical Primer

A chapter-by-chapter mathematical primer for The Geometry of Motion

This volume is organized as a reading path rather than duplicating twelve full chapters in one browser page. Each chapter has its own table of contents, canonical URL, reader notes, and focused review surface.

Foundations

  1. A Primer on Linear Algebra
  2. The Transition to State Space
  3. Configuration Space and Degrees of Freedom
  4. Rotations, Quaternions, and SO(3)
  5. Twists, Wrenches, and the Screw Axis
  6. Exponential Coordinates and Matrix Logarithms

Dynamics and Computation

  1. Recursive Algorithms
  2. Spatial Vector Algebra and Inertia
  3. The Product of Exponentials Formula
  4. The Articulated Body Algorithm
  5. Lagrangian Mechanics
  6. Machine Learning and Neural Networks

Continue with Volume I after completing the mathematical primer.