非自旋航天器混沌姿态运动及其参数开闭环控制

研究万有引力场中受大气阻力且存在结构内阻尼的非自旋航天器在椭圆轨道上平面天平动的混沌及其参数开闭环控制问题．在建立数学模型的基础上确定出现混沌的必要条件并数值验证混沌的存在性，提出非线性振动系统混沌运动的参数开闭环控制并应用于控制航天器的混沌姿态运动．

CHAOTIC ATTITUDE MOTION OF NON SPINNING 1)

The chaotic planar motion of rigid spacecraft on an elliptic orbit in the gravitational field with air drag and internal damping and its control are investigated.Research on chaotic attitude motion of spacecraft can not only provide nonlinear dynamics with engineering background, but also furnish the design of spacecraft with a new view point. Controlling chaos is a new frontier of nonlinear dynamics and control engineering. The mathematical model of attitude motion of the spacecraft with a actuator is derived from the Euler equation and the gravitational torque formula. It is a single degree of freedom oscillation system. In the case without control, it can be treated as a Hamiltonian integrable system under small periodic perturbations. The unperturbed system has two heteroclinic orbits connecting two hyperbolic saddle points. The Melnikov method is employed to establish the analytical condition that the perturbed stable and unstable manifolds intersect transversely. Hence the necessary condition of occurring chaos is obtained. For the system satisfying the condition, a numberical example is presented, and both the time history and the phase trajectory indicate the appearance of chaos. For a given control goal, a parametric open pluse closed loop control law is developed based on the local linearization and the pole assignment. The control law is applied to design the actuator propulsion torque such that the spacecraft maintains static attitude or rotates in a given periodic way. The approach is demonstrated to be effective by numerical results.