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Consider the problem of a rigid body rotating in 3D space under gravity with one point fixed. I am particularly curious about the equilibrium state where the body is spinning at a constant angular ...

I intend to learn KAM Theory. Could you please suggest me a good book on KAM Theory to begin with, where main results are discussed with complete proofs. Thank you.

If my thinking is wrong please let me know. I have little knowledge on beyond-college physics. For research purposes, I read a few introductions to these three formalisms of classical mechanics [1,2,...

Let's take a time-periodic Hamiltonian $H(t,x,y)$ on $\mathbb{R}^2$ and apply an arbitrarily small time-independent perturbation to $H$ via $$ \tilde H (t,x,y) = H(t,x,y) + \epsilon V(x,y), $$ where $...

I am starting to work with Hamiltonian Dynamics and I have been taking a look at some of the basic stuff in KAM theory. I have posted part of this question at MSE but as I did not get any response I ...