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Lagrangian and Hamiltonian Mechanics, PH3073, @StAndrews
- Course Outline and Lecture Notes
Chapter1:
Equations of Motion |
- The Principle of Least Action
- Euler-Lagrange Equations
- Connection to Newtonian Mechanics
- General Properties of the Action
- Galilean Invariance
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Chapter2:
Conservation Laws
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- Energy
- Momentum
- Angular Momentum
- Center of Mass
- Symmetries and Conservation Laws
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Chapter3:
Integration of Equations of Motion
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- One-dimensional Motion
- Two-body Problem in 3D
- Kepler Problem / Planetary Motion
- Elastic Scattering by Central Forces
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Chapter4(a), Chapter4(b) :
Canonical Formalism
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- Hamilton-Jacobi Theory
- Relationship to Quantum Mechanics
- Hamilton's Equations
- Canonical Transformations
- Poisson Brackets
- Liouville's Theorem
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- 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
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