Stability Analysis Of Attitude Motion Of Flexible Spacecraft Subjected To Solar Heat Flux

When the spacecraft accomplishes its specific mission,it not only has requirements for the orbit,but also has certain requirements for its attitude.With the enlargement and complication of spacecraft and the limitation of the payload of the vehicle,it was appeared many large flexible structures consisting of thin-walled tubes.These structures have the characteristics of large size,light weight,low stiffness and low specific heat capacity.It makes the spacecraft vulnerable to heat-induced vibration under the effect of solar heat flux,and the coupling between the spacecraft’s attitude motion and the flexible deformation of the flexible attachment and the incident angle of the heat flux leads to a complex rigid-flexible-thermal coupling problem and may affect the attitude stability of the spacecraft.In this paper,the heat conduction equations of the coupling of solar heat flux incident angle with the system attitude motion and flexible deformation are deduced.Based on the Jourdain variational principle,the dynamic equations of flexible spacecraft considering thermal effects are established,and the rigid-flexible-thermal coupling dynamic equations of flexible spacecraft are obtained by the simultaneous heat conduction and dynamic equations.These rigid-flexible-thermal coupling equations are used to deduce the dynamic equations of spin-stabilized flexible spacecraft and non-spinning flexible spacecraft with circular orbits in the gravitational field subjected to the solar heat flux.By decomposing the temperature field of the flexible body,the rigid-flexible-thermal coupling equations of spin spacecraft and non-spin spacecraft are reduced to linear time-varying systems and linear time-invariant systems with periodic coefficients respectively.Numerical examples are used to describes the feasibility of decomposition of the temperature field.In order to investigate the thermally induced attitude stability of flexible spacecraft the concept of input-to-state stability is introduced.Based on the Lyapunov transformation and Floquet theory,it is proved that for the linear time-invariant systems and linear time-varying systems with periodic coefficients the conditionsof input-to-state stability and the Lyapunov stability of the non-input system are equivalent.According to the input-to-state stability criterion of linear time-varying systems with periodic coefficients and linear time-invariant systems,it is analyzed the stability of thermal induced vibration of flexible attachments of non-spinning and spinning spacecraft and thermal induced attitude motion of flexible spinning spacecraft and non-spinning spacecraft which are subjected to the solar heat flux.The results of the paper show that it is difficult for the flexible attachment on the non-spinning spacecraft to suffer thermal chatter due to the effect of structural damping,however,thermal chatter may occur for axial booms on spinning-stabilized spacecraft.For the flexible spinning-stabilized spacecraft subjected to the heat flux,the attitude motion will be stable when the spinning velocity satisfies certain conditions,otherwise it may become unstable.The relative motion of the flexible spacecraft with circular orbit in a gravitational field may also be unstable under heat flow.However,because of the long cycle of the motion of the oscillate and the effect of damping,it is difficult to lose stability in practical situations.