References for Lagrangian and Hamiltonian mechanics

Question

What are good references for learning about Lagrangian and Hamiltonian mechanics, for someone with a mathematical background?

Mathematically I'm learning and working on holomorphically symplectic manifolds/projective varieties, and I would like to understand the physical background, which is classical mechanics. Can anyone suggest a reference for learning mechanics, which a mathematician might enjoy?

Answer 1

For Hamiltonian Mechanics there are actually quite a few books from the mathematical point of view. I personally really like

• G. Rudolph, M. Schmidt: Differential Geometry and Mathematical Physics. Part I. Manifolds, Lie Groups and Hamiltonian Systems, Springer, 2013.

This books also contains a lot of background material from differential and symplectic geometry. Furthermore, you might be interested in

• T. Lee, M. Leok and H. McClamroch: Global Formulations of Lagrangian and Hamiltonian Dynamics on Manifolds, A Geometric Approach to Modeling and Analysis, Springer, 2018.

Last but not least, you might have a look at

• A. Knauf: Mathematical Physics: Classical Mechanics, Springer, 2018.

This book is not only for Lagrangian and Hamiltonian mechanics, but also contains many other topics of classical mechanics in a mathematical precise language.

There are of course also much more books on this topic out there, for example also the classical book by V. Arnold mentioned in the comments. The books above a just books, which I personally really like and which seem to be not so well known compared to other more classical references.