Ongoing
From Symplectic Structures to Symmetry
Introduction to Geometric Mechanics
CONTENTS
Contents
- CHAPTER01→
Symplectic Geometry: The Natural Language of Classical Mechanics
Starting from Hamilton’s equations, understand why the symplectic form captures the structure of classical dynamics more directly than coordinates.
- CHAPTER02→
The Hamilton–Jacobi Equation and Lagrangian Submanifolds
View the action as a generating function and understand how families of classical trajectories become geometric objects in phase space.
- CHAPTER03→
Momentum Maps and Noether’s Theorem
How symmetries generate conserved quantities on symplectic manifolds, and why Lie group actions provide the right framework.