Lagrangian and Hamiltonian Mechanics, PH3073, @StAndrews

  • Course Outline and Lecture Notes


    Equations of Motion
    • The Principle of Least Action
    • Euler-Lagrange Equations
    • Connection to Newtonian Mechanics
    • General Properties of the Action
    • Galilean Invariance


    Conservation Laws
    • Energy
    • Momentum
    • Angular Momentum
    • Center of Mass
    • Symmetries and Conservation Laws


    Integration of Equations of Motion
    • One-dimensional Motion
    • Two-body Problem in 3D
    • Kepler Problem / Planetary Motion
    • Elastic Scattering by Central Forces

    Chapter4(a), Chapter4(b) :

    Canonical Formalism
    • Hamilton-Jacobi Theory
    • Relationship to Quantum Mechanics
    • Hamilton's Equations
    • Canonical Transformations
    • Poisson Brackets
    • Liouville's Theorem

  • Books recommended as core/background reading

    • Mechanics: Volume 1 (Course of Theoretical Physics), L. D. Landau and E.M. Lifshitz, Butterworth-Heinemann
      Very nice book and inexpensive!

    • Theoretical Mechanics of Particles and Continua, John Dirk Walecka, Alexander L. Fetter, Dover Publications Inc.
      My personal favorite. Used to be very expensive but now availabe at Dover.

    • Classical Mechanics, Herbert Goldstein, Charles P. Poole Jr., John L. Safko, Pearson Education