  We propose a perturbation algorithm for Hamiltonian systems on a Lie algebra
$\mathbb{V}$, so that it can be applied to non-canonical Hamiltonian systems.
Given a Hamiltonian system that preserves a subalgebra $\mathbb{B}$ of
$\mathbb{V}$, when we add a perturbation the subalgebra $\mathbb{B}$ will no
longer be preserved. We show how to transform the perturbed dynamical system to
preserve $\mathbb{B}$ 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.
