Nonlinear attitude motion near resonance.

Abstract

The roll-yaw attitude motion of a spinning symmetric satellite in an elliptic orbit has been investigated with particular emphasis on the behavior near resonance. Resonance will occur when there is a low-order commensurability between the frequencies of the two normal modes of the attitude motion or between these attitude frequencies and the orbital mean motion. The first situation is termed internal resonance; the second, external resonance. The principal feature near internal resonance consists of a long-period interchange of energy between the two normal modes. This interchange depends upon the initial amplitude and phase, the initial partition of the energy between the two modes, and the deviation from exact resonance. Assuming certain types of initial conditions, sufficient conditions for this interchange to be small are derived. Near external resonance, the long-period growth or interchange of energy between modes is small, provided there is a sufficiently large detuning from an exact commensurability. Stability inequalities are derived in terms of this detuning, the natural frequencies of the normal modes, and certain constants. For both situations a measure of the width of the resonance bands is obtained and regions of minimal sensitivity along a resonance line are noted. Finally, the determination of stable and unstable periodic attitude motions is outlined.