Analytical Mechanics for Relativity and Quantum Mechanics

  • INTRODUCTION: THE TRADITIONAL THEORY
    • Basic Dynamics of Point Particles and Collections
    • Introduction to Lagrangian Mechanics
    • Lagrangian Theory of Constraints
    • Introduction to Hamiltonian Mechanics
    • The Calculus of Variations
    • Hamilton’s Principle
    • Linear Operators and Dyadics
    • Kinematics of Rotation
    • Rotational Dynamics
    • Small Vibrations About Equilibrium
  • MECHANICS WITH TIME AS A COORDINATE
    • Lagrangian Mechanics with Time as a Coordinate
    • Hamiltonian Mechanics with Time as a Coordinate
    • Hamilton’s Principle and Noether’s Theorem
    • Relativity and Spacetime
    • Fourvectors and Operators
    • Relativistic Mechanics
    • Canonical Transformations
    • Generating Functions
    • Hamilton–Jacobi Theory
  • MATHEMATICAL APPENDICES
    • Vector Fundamentals
    • Matrices and Determinants
    • Eigenvalue Problem with General Metric
    • The Calculus of Many Variables
    • Geometry of Phase Space