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Hamiltonian mechanics

Table of contents

Action-angle coordinates

Arnold–Givental conjecture

Canonical transformation

Fundamental vector field

Generating function (physics)

Geometric mechanics

Hamilton's optico-mechanical analogy

Hamiltonian fluid mechanics

Hamiltonian system

Hamiltonian vector field

Hamilton–Jacobi equation

Hamilton–Jacobi–Einstein equation

Integrable system

Jacobi coordinates

Kolmogorov–Arnold–Moser theorem

Lagrange, Euler, and Kovalevskaya tops

Lagrange bracket

Liouville's theorem (Hamiltonian)

Liouville–Arnold theorem

List of common coordinate transformations

Mathieu transformation

Minimal coupling

Momentum map

Monogenic system

Non-autonomous mechanics

Phase space

Phase space crystals

Poisson bracket

Primary constraint

Reversible reference system propagation algorithm

Superintegrable Hamiltonian system

Swinging Atwood's machine

Symmetry in Mechanics

Symplectic integrator

Symplectomorphism

Tautological one-form

Weinstein conjecture

 Ancestors (5)

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Hamiltonian mechanics by

Ciro Santilli 32 Updated 2024-09-15 Created 1970-01-01

Equivalent to Lagrangian mechanics but formulated in a different way.

Motivation: Lagrangian vs Hamiltonian.

TODO understand original historical motivation, www.youtube.com/watch?v=SZXHoWwBcDc says it is from optics.

Intuitively, the Hamiltonian is the total energy of the system in terms of arbitrary parameters, a bit like Lagrangian mechanics.

Bibliography:

www.damtp.cam.ac.uk/user/tong/dynamics/four.pdf

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