Nonlinear Phenomena in Complex Systems, 1999, Vol.2, No.2, pp.96--101

NONLINEAR PHENOMENA IN COMPLEX SYSTEMS
An Interdisciplinary Journal

1999, Volume 2, Number 2, pp.96--101

Lissajous Solutions of the Satellite Oscillation Equation: Stability and Bifurcations via Higher Order Averaging.
Sergey Sadov

The equation of plane oscillations of a satellite is a Hamiltonian system with one degree of freedom and 2Pi-periodic dependence on time and on x₁. It contains two parameters Eps and e, one of which (Eps) is small. The unperturbed system is linear. Solutions that correspond to cycles of the Poincare map on a cylinder (x₁ mod 2Pi, x₂) are called Lissajous solutions. Their stability and bifurcations with parameter e changing are studied by the averaging method. It is shown how degenerate cases, where calculation of higher order terms is needed, arise in a natural way. Sufficient truncations of the normal form for those cases are described.

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