Coupling dynamic characteristics of simplified model for tethered satellite system

Abstract: The evolution of the attitude angle and the mechanical energy exchange between the bus system and the solar sail via the connecting wires are the main manifestations of the coupling dynamic effects on the orbit evolution, the attitude adjusting and the flexible vibration of the tethered satellite system. To investigate attitude evolution of the tethered system and the mechanical energy transfer/loss characteristics between the bus system and the solar sail via the connecting wires, a structure-preserving method is developed in this paper. Simplifying the tethered satellite system as a composite structure consisting of a particle and a flexible thin panel connected by four special springs, the dynamic model is deduced via the Hamiltonian variational principle firstly. Then, a structure-preserving approach that connects the symplectic Runge–Kutta method and the multi-symplectic method is developed. The excellent structure-preserving property of the numerical scheme constructed is presented to illustrate the credibility of the numerical results obtained by the constructed structure-preserving approach. From the numerical results on the mechanical energy transfer/loss in the composite structure, it can be found that the mechanical energy transfer tendency in the tethered system is dependent of the initial attitude angle of the system while the total mechanical energy loss of the system is almost independent of the initial attitude angle. In addition, the special stiffness range of the spring is found in the attitude angle evolution of the system, which provides a structural parameter design window for the connecting wires, that is, the duration needed to arrive the stable attitude is short when the stiffness of the wire is designed in this special range. Graphic Abstract: The evolution of the attitude angle and the mechanical energy exchange between the bus system and the solar sail via the connecting wires are the main manifestations of the coupling dynamic effects on the orbit evolution, the attitude adjusting and the flexible vibration of the tethered satellite system. To investigate attitude evolution of the tethered system and the mechanical energy transfer/loss characteristics between the bus system and the solar sail via the connecting wires, a structure-preserving method is developed in this paper. Simplifying the tethered satellite system as a composite structure consisting of a particle and a flexible thin panel connected by four special springs, the dynamic model is deduced via the Hamiltonian variational principle firstly. Then, a structure-preserving approach that connects the symplectic Runge-Kutta method and the multi-symplectic method is developed. The excellent structure-preserving property of the numerical scheme constructed is presented to illustrate the credibility of the numerical results obtained by the constructed structure-preserving approach. From the numerical results on the mechanical energy transfer/loss in the composite structure, it can be found that the mechanical energy transfer tendency in the tethered system is dependent of the initial attitude angle of the system while the total mechanical energy loss of the system is almost independent of the initial attitude angle. In addition, the special stiffness range of the spring is found in the attitude angle evolution of the system, which provides a structural parameter design window for the connecting wires, that is, the duration needed to arrive the stable attitude is short when the stiffness of the wire is designed in this special range.[Figure not available: see fulltext.]