Dynamics and control of artificial satellite orbits with multiple tesseral resonances

Todd Allan Ely, Purdue University

Abstract

Eccentric and inclined resonant orbits exhibit complex motions that have the potential to become chaotic. Furthermore, these complex motions may also destabilize classical control strategies. Understanding the mechanisms that cause such motions to occur is crucial. Utilizing a variety of analytical techniques from nonlinear Hamiltonian systems theory, it is determined that, at most inclinations and eccentricities, resonant tesseral harmonics can interact to produce chaotic responses in the semi-major axis and the stroboscopic mean node (primary variables of interest in east-west stationkeeping) of an orbit. These results are verified with numerically propagated trajectories and Poincare sections. Furthermore, resonance overlap occurs between interacting lunar harmonics. This overlap result can produce significant excursions in eccentricity. Also, the potential for diffusion between the eccentricity (or inclination) and semi-major axis exists because of the coupling introduced by the tesseral harmonics. However, the interaction between these two modes (motion in eccentricity and motion in semi-major axis) is slight for orbits with periods of 12 hr or lower. It is concluded that the qualitative motion of the semi-major axis and the node, on time scales of interest for mission planning, evolves primarily from tesseral harmonic effects. Also presented is an investigation of the local chaotic behavior near the separatrix of the primary tesseral term as inclination decreases from the critical value. Using techniques similar in form to Melnikov methods, a sufficient condition for the width of the local chaotic layer is obtained, and is compared to numerical simulations. From these insights into the dynamics, it is demonstrated that the classical method for east-west stationkeeping of the stroboscopic mean node may not be stable for the class of orbits considered here. A stable control method is developed that can adapt to the changing dynamical environment introduced by these complex and/or chaotic orbits. As with the classical approach, it utilizes a 'grazing' strategy that minimizes stationkeeping costs by maximizing time between maneuvers.

Degree

Ph.D.

Advisors

Howell, Purdue University.

Subject Area

Aerospace materials

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