Analytical Dynamics

Classical Mechanics in 22 chapters — from “Configuration Space and the Geometry of Motion” to “Stability Theory: Linearization, Floquet Theory, and Arnold Diffusion”.

Chapters

  1. Configuration Space and the Geometry of Motion
  2. Newton’s Laws and the Newtonian Program
  3. The Principle of Stationary Action
  4. Lagrangian Mechanics: Formalism and First Applications
  5. Noether’s Theorem and the Deep Structure of Conservation
  6. Rotational Kinematics: The Geometry of SO(3)
  7. Rigid Body Dynamics I: Inertia Tensor and Euler’s Equations
  8. Rigid Body Dynamics II: The Heavy Symmetric Top
  9. Small Oscillations and the Eigenvalue Problem
  10. Driven and Damped Oscillations: Resonance and Response
  11. Perturbation Theory and Secular Effects
  12. The Hamiltonian Formulation: Phase Space and Canonical Equations
  13. Symplectic Geometry and Liouville's Theorem
  14. Canonical Transformations and Generating Functions
  15. Hamilton-Jacobi Theory: Action as a Function
  16. Integrability and the Liouville-Arnold Theorem
  17. Central Force Motion and Orbital Mechanics
  18. The Three-Body Problem and the Onset of Chaos
  19. Perturbation Theory for Nearly Integrable Systems
  20. KAM Theory and the Persistence of Invariant Tori
  21. Chaos, Lyapunov Exponents, and Sensitive Dependence
  22. Stability Theory: Linearization, Floquet Theory, and Arnold Diffusion