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I'm looking for books / articles that provide rigorous formulations of Hamiltonian mechanics on Manifolds. I found the book "Global Formulations of Lagrangian and Hamiltonian Dynamics on Manifolds" [1] by Lee, Leok and McClamroch, but I'm looking for more references.

My goal is to study the math behind those formulations and what problems still demand rigorous definitions.

[1] - http://www.math.ucsd.edu/~mleok/pdf/LHDynamics.pdf

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  • $\begingroup$ Any book on classical mechanics will deal with it: two examples are 1. Goldstein 2. Gantmacher $\endgroup$ – gented May 27 at 19:54
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Another good reference:

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Arnold' work is great. The Russian school of writing a textbook. More abstract and more comprehensive is the American "bible" on mathematical mechanics>

Abraham & Marsden, "Foundations of Mechanics".

https://www.amazon.com/Foundations-Mechanics-2nd-Ralph-Abraham/dp/080530102X

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