Modal control of an unstable periodic orbit

Details Modal control of an unstable periodic orbit Modal control of an unstable periodic orbit

Mar 1983

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1983jansc..31...63w&link_type=abstract

Journal of the Astronautical Sciences (ISSN 0021-9142), vol. 31, Jan.-Mar. 1983, p. 63-76.

Astronomy and Astrophysics

Astronomy

1

Floquet Theorem, Satellite Control, Satellite Orbits, Satellite Perturbation, Stationkeeping, Control Theory, Equations Of Motion, Periodic Functions, Perturbation Theory, Poincare Problem

Scientific paper

Floquet theory is applied to the problem of designing a control system for a satellite in an unstable periodic orbit. Expansion about a periodic orbit produces a time-periodic linear system, which is augmented by a time-periodic control term. It is shown that this can be done such that (1) the application of control produces only inertial accelerations, (2) positive real Poincareexponents are shifted into the left half-plane, and (3) the shift of the exponent is linear with control gain. These developments are applied to an unstable orbit near the earth-moon L(3) point pertubed by the sun. Finally, it is shown that the control theory can be extended to include first order perturbations about the periodic orbit without increase in control cost.

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