Canonical Floquet Theory II: Action-Angle Variables Near Conservative Periodic Orbits
Classical Floquet theory describes motion near a periodic orbit. But comparing Floquet theory to action angle methods shows which Jordan form is desirable. A new eigenvector algorithm is developed ensuring a canonical transform and handling the typical for the case of repeated eigenvalues, a chronic problem in conservative Hamiltonian systems. This solution also extends the Floquet decomposition to adjacent trajectories, and is fully canonical. This method yields the matrix of frequency partial derivatives, extending the solution’s validity. Some numerical examples are offered.
Journal of the Astronautical Sciences
Wiesel, W. E. (2021). Canonical floquet theory II: Action-angle variables near conservative periodic orbits. Journal of the Astronautical Sciences, 68, 391–401. https://doi.org/10.1007/s40295-021-00258-z