Lectures on Classical Mechanics (original) (raw)

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This work provides an in-depth exploration of classical mechanics, contrasting the Newtonian framework with Lagrangian mechanics. It discusses the enduring relevance of classical mechanics in physics and engineering, despite advancements in general relativity and quantum mechanics. The text introduces various concepts like kinetic energy, Hamilton-Jacobi equations, and configuration/phase space, emphasizing their significance in the broader context of physics.

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References (4)

  1. 6 (May 2, 4, 6)-From Lagrangians to Hamiltonians, continued. Regular and strongly regular Lagrangians. The cotangent bundle as phase space. Hamilton's equa- tions. Getting Hamilton's equations directly from a least action principle. Week 7 (May 9, 11, 13)-Waves versus particles: the Hamilton-Jacobi equation.
  2. Hamilton's principal function and extended phase space. How the Hamilton-Jacobi equa- tion foreshadows quantum mechanics. Week 8 (May 16, 18, 20)-Towards symplectic geometry. The canonical 1-form and the symplectic 2-form on the cotangent bundle. Hamilton's equations on a symplectic manifold. Darboux's theorem. Week 9 (May 23, 25, 27)-Poisson brackets. The Schrödinger picture versus the Heisenberg picture in classical mechanics. The Hamiltonian version of Noether's theorem. Poisson algebras and Poisson manifolds. A Poisson manifold that is not symplectic. Liouville's theorem. Weil's formula. Week 10 (June 1, 3, 5)-A taste of geometric quantization. Kähler manifolds. If you find errors in these notes, please email me! I thank Sheeyun Park and Curtis Vinson for catching lots of errors. Bibliography
  3. Peter Peldan. Actions for gravity, with generalizations: A review. Classical and Quantum Gravity, 11:1087, 1994.
  4. J. A. Wheeler, K. S. Thorne, and C. W. Misner. Gravitation. W. H. Freeman, New York, 1971.