Symplectic Connections and the Linearization of Hamiltonian Systems
Marsden, J. E., T. S. Ratiu and G. Raugel
Proc. Roy. Soc. Ed. A, 117, 329-380
Abstract:
This paper uses symplectic connections to give a Hamiltonian structure to
the first variation equation for a Hamiltonian system along a given dynamic
solution. This structure generalises that at an equilibrium solution
obtained by restricting the symplectic structure to that point and using
the quadratic form associated with the second variation of the Hamiltonian
(plus Casimir) as energy. This structure is different from the well-known
and elementary tangent space construction. Our results are applied to
systems with symmetry and to Lie-Poisson systems in particular.