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Analytical Mechanics I

Reconstructing Lagrangian and Hamiltonian mechanics in the language of manifolds and differential forms, beyond the engineer's textbook approach.

Table of contents

  1. Chapter 0 Mathematical preliminaries — a toolbox for manifold mechanics
  2. Chapter 1 Equations of motion — from Newton to generalized coordinates
  3. Chapter 2 Constrained motion on surfaces — constraints and Lagrange multipliers
  4. Chapter 3 Tensors and the covariant derivative — keeping equations the same under coordinate change
  5. Chapter 4 Manifolds — spaces that are locally flat
  6. Chapter 5 Vector fields and flows — the tools that draw time evolution
  7. Chapter 6 Differential forms — what integrals are really made of
  8. Chapter 7 Lagrangian mechanics — a function on $TM$ that determines motion
  9. Chapter 8 Variational principle — paths that make the action stationary
  10. Chapter 9 Symmetry and conservation — Noether's theorem
  11. Chapter 10 Hamiltonian mechanics — pivoting to phase space
  12. Chapter 11 Canonical transformations — the art of choosing good coordinates
  13. Chapter 12 Poisson brackets and integrability