Abstract
The Euler dynamical equation which describes the attitude motion of a rigid body will exhibit very complex dynamic behaviors under the action of different external torques. Many special types of new chaotic attractors are presented, including hidden attractors, double-body-double-core chaotic attractors, and single-body-three-core-tree-wing chaotic attractors. The position of equilibrium points in several typical cases of the Euler dynamic equation is solved, and the stability of linearized equation at each equilibrium point and its influence on the formation of the chaotic attractor are analyzed. An improved nonlinear relay control law based on Euler angle feedback is developed to stabilize a new chaotic spacecraft attitude motion to an appointed equilibrium point or a periodic orbit.
Highlights
Multifarious Chaotic AttractorsEquation (7) is a more generalized 3-dimensional nonlinear system which will exhibit complex (periodic, quasiperiodic, or chaotic) dynamic behaviors under the action of different external torques
Mathematical Problems in Engineering rotation rate and not to rotate along the other two axes
The Attitude Motion Equations of a Rigid Body e attitude motion of a rigid body could be described by the Eulerian equations, which consists of kinematic equations and dynamic equations
Summary
Equation (7) is a more generalized 3-dimensional nonlinear system which will exhibit complex (periodic, quasiperiodic, or chaotic) dynamic behaviors under the action of different external torques. Ω_ y ω_ z cωx − ωy − ωxωz −bωz + ωxωy. Ese torques are chosen to be sufficiently large to induce chaotic motion and are comparable in magnitude with the available thruster torques. E dynamics of the satellite will exhibit chaotic motion.
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