Action-angle variables near degenerate periodic orbits

Authors

William E. Wiesel, Air Force Institute of Technogy

Document Type

Conference Proceeding

Publication Date

8-19-2018

Abstract

Classical Floquet theory describes motion near a periodic orbit. However, there is a missing piece in the Floquet solution. A different Jordan normal form allows the decoupling of modal dynamics near the periodic orbit, and not just on the periodic orbit. A new eigenvector solution is offered in the case of repeated eigenvalues. This solution extends the Floquet decomposition to adjacent trajectories, and is fully canonical. This also yields the matrix of frequency partial derivatives, extending the solution’s validity. Some numerical examples are offered.

Comments

© 2018 Univelt.

Published in Volume 167 of Advances in the Astronautical Sciences. ISBN 978-087703657-9

Source Publication

2018 AAS/AIAA Astrodynamics Specialty Conference

Recommended Citation

Wiesel, W. E. (2018). Action-angle variables near degenerate periodic orbits. AAS/AIAA Astrodynamics Specialist Conference, 2018, Advances in the Astronautical Sciences 167, 3–14.