The Geometry of Motion

A Multi-Volume Series on the Mathematics of Movement

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Mathematical and computational foundations for rigid-body dynamics, control, biomechanics, neural control, and simulation

Preface

The Geometry of Motion is an in-development multi-volume series on the mathematics of movement. It begins with rigid-body kinematics and dynamics, then extends through nonlinear control, biomechanics, neural control, and computational simulation.

The series is meant to connect formal derivation with interpretation. Each volume focuses on a coherent technical theme, but the notation and examples are intended to carry across volumes so that concepts can be revisited from several angles.

NoteStatus Note

This series is still under active development. Some volumes are more mature than others, and the PDF and HTML editions are not always identical in figure support or layout. Volumes 0 and I have separate HTML chapter pages; Volume II is a combined HTML monograph. Volumes III–V have PDF editions and canonical LaTeX sources, without separate HTML chapter editions here. Follow the edition links below.

Volumes & Table of Contents

Volume 0: The Mathematical Primer

Volume I: Tangent-Space Methods for Nonlinear Control

Volume II: Control Is Motion

Volumes III–V (PDF Editions)

  • Volume III: Biomechanics - Biology to Systems (PDF edition) (PDF and LaTeX; no separate HTML chapter edition here.)
  • Volume IV: Human Motor Control (PDF edition) (PDF and LaTeX; no separate HTML chapter edition here.)
  • Volume V: Practical Application (PDF edition) (PDF and LaTeX; no separate HTML chapter edition here.)

How to Read the Series

Start with Volume 0 if you want the mathematical background.

Start with Volume I if your main interest is tangent-space methods, nonlinear control, and the site’s control-theoretic claims.

Use Volume II and later volumes when you want the application-facing material on movement, biomechanics, neural control, and simulation.

Note on Editions

Some figures, especially diagram-heavy PDF material, render better in the PDF edition than in the HTML edition. Where the HTML edition uses simplified substitutes, the underlying text remains the primary source of the argument.

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  author = {},
  title = {The {Geometry} of {Motion}},
  url = {https://affinedrift.com/articles/The_Geometry_of_Motion/quarto/},
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