Nonlinear dynamics of the planar pitch attitude motion for a gravitygradient satellite
Abstract
The nonlinear dynamics of the planar pitch attitude motion for a gravitygradient satellite in an elliptical orbit about a central body are investigated using phase diagrams, Poincare' maps, bifurcation plots, spectral density plots, Lyapunov exponents, and chaos diagrams. The satellite is assumed to be a rigid body influenced only by torques from an inversesquare gravitational field, and its major axis is assumed to be normal to the orbit plane. The resultant planar pitching motion is either periodic, quasiperiodic, or chaotic, depending upon the values of the system parameters, eccentricity and satellite inertia ratio. The relationships of the system parameters to the nonlinearity of the system are explored with chaos diagrams, which incorporate the results of the Lyapunov exponent calculations into a useful tool for predicting the onset of chaotic motion in parameter space. The border between regular and chaotic motion in the chaos diagrams is shown to be fractal. The dynamics of the basic problem supplemented by the addition of damping terms and an oblate, axially symmetric central body are also investigated. Strange attractors are found and the validity of Melnikov's method to predict the border between chaos and regular motion is examined.
 Publication:

Final Report
 Pub Date:
 August 1994
 Bibcode:
 1994pafb.rept.....K
 Keywords:

 Attitude (Inclination);
 Elliptical Orbits;
 Exponents;
 Gravitational Fields;
 Gravity Gradient Satellites;
 Nonlinearity;
 Phase Diagrams;
 Rigid Structures;
 Torque;
 Axisymmetric Flow;
 Damping;
 Eccentricity;
 Fractals;
 Inertia;
 Pitching Moments;
 Strange Attractors;
 Spacecraft Design, Testing and Performance