Hamiltonian Perturbation Theory on a Lie Algebra. Application to a non-autonomous Symmetric Top - Valvo, Lorenzo; Vittot, Michel (Discontinuity, Nonlinearity, and Complexity, 2026)
We propose a perturbation algorithm for Hamiltonian systems on a Lie algebra V, so that it can be applied to non-canonical Hamiltonian systems. Given a Hamiltonian system that preserves a subalgebra B of V, when we add a perturbation the subalgebra B will no longer be preserved. We show how to transform the perturbed dynamical system to preserve B up to terms quadratic in the perturbation. We apply this method to study the dynamics of a non-autonomous symmetric Rigid Body. In this example our algebraic transform plays the role of Iterative Lemma in the proof of a KAM-like statement.