Classical mechanics
Introductory
Goldstein et al, Classical Mechanics
Arnold, Mathematical Methods of Classical Mechanics
Intermediate
Jose and Saletan, Classical dynamics: A contemporary approach
Landau and Lifschitz, Mechanics
Cushman and Bates, Global aspects of classical integrable systems
Advanced
Marsden and Ratiu, Introduction to mechanics and symmetry
Abraham and Marsden, Foundations of Mechanics
Spivak, Physics for mathematicians: Mechanics
Abraham, Marsden, Ratiu, Manifolds, tensor analysis and applications
Liebermann and Marle, Symplectic geometry and analytical mechanics
Souriau et al, Structure of dynamical systems: a symplectic view of physics
Guillemin & Sternberg, Symplectic techniques in physics
Ortega and Ratiu, Momentum maps and Hamiltonian reduction
Audin, Torus actions on symplectic manifolds
Marsden, Misiolek, Ortega, Perlmutter, Ratiu, Hamiltonian reduction by stages
Audin, Silva, Lerman, Symplectic geometry of integrable Hamiltonian systems
Relevant mathematics:
- Lagrangian formulation: differential geometry, jet bundles and calculus of variations
- Hamiltonian formulation and symplectic reduction: symplectic and Poisson geometry
- Noether theorems: Jet bundles and geometric ODEs & PDEs , Lie algebras and Lie groups, Lie group actions on manifolds
- ODEs and continuous dynamical systems