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15: Advanced Hamiltonian Mechanics

Last updated

Nov 21, 2020
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- 14.S: Coupled linear oscillators (Summary)
- 15.1: Introduction to Advanced Hamiltonian Mechanics

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15.1: Introduction to Advanced Hamiltonian Mechanics
Hamiltonian mechanics underlies both classical and quantum physics.
15.2: Poisson bracket Representation of Hamiltonian Mechanics
The Poisson bracket representation of Hamiltonian mechanics provides a direct link between classical mechanics and quantum mechanics.
15.3: Canonical Transformations in Hamiltonian Mechanics
Hamiltonian mechanics is an especially elegant and powerful way to derive the equations of motion for complicated systems. Integrating the equations of motion to derive a solution can be a challenge. Hamilton recognized this difficulty, so he proposed using generating functions to make canonical transformations which transform the equations into a known soluble form.
15.4: Hamilton-Jacobi Theory
The Hamilton-Jacobi theory uses a canonical transformation of the Hamiltonian to a solvable form. Relate surfaces of constant action integral to corresponding particle momenta.
15.5: Action-angle Variables
Canonical transformation to action-angle variables provides a solution.
15.6: Canonical Perturbation Theory
Use perturbation theory to solve three-body systems.
15.7: Symplectic Representation
The symplectic representation provides an elegant but appropriate description.
15.8: Comparison of the Lagrangian and Hamiltonian Formulations
Their relative merits.
15.E: Advanced Hamiltonian Mechanics (Exercises)
15.S: Advanced Hamiltonian mechanics (Summary)

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