Spivak Michael. Physics for Mathematicians. Mechanics I

Publish or Perish, 2010. — 733 p.The Foundations of Mechanics.Newtonian Mechanics.
Newton's Analysis of Central Forces.
Conservation Laws.
The One-Body and Two-Body Problems.
Rigid Bodies.
Constraints.
Philosophical and Historical Questions.Building on the Foundations.Oscillations.
Rigid Body Motion.
Non-Inertial Systems and Fictitious Forces.
Friction, Friend and Foe.Lagrangian Mechanics.Analytical Mechanics.
Variational Principles.
Small Oscillations.Interlude.Light.Hamiltonian Mechanics.The Cotangent Bundle.
The Interplay of Mechanics and Optics.
Hamilton-Jacobi Theory.
Canonical Transformations.
Symplectic Manifolds.
Liouville Integrability.
Epilogue.Supplement. A PDE Primer.