Researchs On The Energy Conserving Algorithm With Dynamic Analysis Of Space Solar Power Station

The phenomenon of nonlinearity,which is widely distributed in nature,engineering and social life,is one of the most important characteristics of the complex dynamic system.Mechanical equations are the most used ways to describe those phenomena,and these equations are strong-nonlinearity,high-dimension and coupled.Meanwhile,as the systems are more complex,the exact solutions of these systems are not so easy to obtain.On the one hand,from the view of science,how to solve those nonlinear dynamic equations has attracted lots of researchers at home and abroad.Meanwhile,in recent years,with the rapid advancement of the technology of aerospace science,how to establish the dynamic model for very large spacecraft,such as space laboratory,space solar power station(SSPS)and so on,and to solve these complex systems with high efficiency are the most important tasks and challenges in engineering technology.Furthermore,strong nonlinearity and high dimension are two of important characteristics of these large spacecraft.On the other hand,although plenty of studies have been done to investigate the nonlinear dynamic mechanics theoretically and numerically,it is clear that further theoretical development for establishing the dynamic model is required to meet the needs of SSPS.Based on the aforementioned view,in this thesis,the energy conserving algorithm have been developed to study the nonlinear dynamic equations of SSPS,the theoretical models of SSPS have been established,the orbit,attitude and vibration dynamics model of SSPS have been researched,the numerical methods have been constructed,and numerical simulations of SSPS have been carried out and analyzed.Meanwhile,the simulated numerical results validate the analytical models and proposed methods and superiority of the numerical methods in this thesis.Some conclusions have potential applications for the design of SSPS.The main content of this dissertation is organized as follows:1.A generalized numerical method of conserving energy and constraint of systems has been developed for the constrained Hamiltonian systems,which is one of the basic systems for SSPS.Based on the Zu Chong-zhi method and the the Verlet method,a new numerical format is developed for the differential equations.Then the constraint equations are discretized directly into discrete algebraic equations,which are solved by using Newton-Raphson iterative method.The proposed method is proved to conserve energy and constraint of system.Numerical simulations are carried out to verify the proposed method in this dissertation.By comparing the results with other results in literatures,it is easily found that the proposed method not only can conserve the energy but also constraints of the system.Meanwhile,the results also show that the proposed method has high accuracy and efficiency.Thus,the numerical method can be applied to study the dynamic response of SSPS.2.The differential-algebraic equations are used to describe the dynamic equations of SSPS,and the default of the displacement constraint has always happened in numerical simulations of SSPS.Thus,based on the projection technique and the Runge-Kutta method,the projected Runge-Kutta method is developed for the issue of the complete constraint Hamilton system.The proposed method not only maintains displacement constraint,velocity constraint,acceleration constraint,but also the total energy of the system.By introducing a standard Lagrangian multiplier,and based on the projection of a 3 stage 6 order implicit Runge-Kutta method,the numerical format for that problem is established through correction of constraint violation and energy dissipation.The effectiveness of the proposed numerical method is verified by the numerical experiments.The numerical results show that the proposed method is more stable than the traditional method.Meanwhile,the proposed method can also maintain levels of constraints and energy system at the same time.That can conserve constraints at all kinds of levels and the energy of tethered satellites system will not drift.3.Based on the symplectic method,the orbital dynamic behaviors of abacus,sail tower and tethered SSPS are investigated,which have taken the earth shadow and effective cross-sectional area of SSPS into consideration.An analytical model has been established.Firstly,the dynamic equations in Largrangian system are derived by using the symplectic conserving method.Secondly,by using the Legendre transformation and introducing the generalized momenta,the dynamic equations are transformed into Hamiltonian system,and the corresponding canonical equations of the orbit of SSPS are derived.The symplectic Runge-Kutta method has been used to solve these canonical equations of the orbit of SSPS.Finally,the effectiveness of the proposed model and superiority of the symplectic Runge-Kutta method are verified through the numerical results and analysis.The numerical results show that the effects of the earth shadow and the effective cross-sectional area variations on SSPS are significant.Meanwhile,the curves of the semi-major axis,eccentricity and orbital inclination in geosynchronous orbit are plotted.The results of this paper might have potential applications for the design of SSPS.4.The SSPS has the characteristics of super large,super soft,and the large deformation coupled with the motion of SSPS itself.So,traditional modeling methods have some defects.Comparing with the traditional modeling theory,the absolute nodal coordinate formulation(ANCF)for SSPS is one of most important modeling theories for SSPS.The theory not only overcomes the limitation of those classical modeling theories,but also the equations established by the ANCF have several advantages,such as constant mass matrix of the system,no Coriolis force and centrifugal force term and so on.Based on the ANCF,the dynamic behavior of solar panels of a tethered SSPS has been investigated in orbit.The solar panel is tight tethered constraints.On the basis of planar motion model,by using Legendre transformation and introducing generalized momenta,the constrained Hamiltonian equations of coupled orbital motion,attitude motion and structural vibration of SSPS are derived.The proposed method—projected Runge-Kutta method has been adopted to solve the differential-algebraic equations.Numerical results confirm the validity of present modeling theory and numerical method.The numerical results also reveal that the constraints and energy of SSPS are well preserved.Meanwhile,the effects of the tether length,bus mass and orbital altitude on the dynamic behaviors of the tethered SSPS are discussed.5.The integrated symmetrical concentrator system(ISC)has a dimension of km scale,and the design of microwave antenna and layout of the array of solar cell can reduce the mass and volume of the power transmission system.Considering the influence of the nonspherical gravitational forces on the ISC,the dynamic model of the ISC has been established.Based on the symplectic conserving method,the dynamic equations are derived.The Legendre transformation is used and the generalized momenta is introduced,the coupled orbital,attitude and structural Hamiltonian equations of the ISC are constructed by using the Legendre transformation and introducing the generalized momenta.Then,the symplectic Runge-Kutta method is applied to solve the coupled dynamic equations of the ISC.Numerical examples are analyzed to verify the analytical model proposed in the present thesis and the effectiveness of the proposed method.Meanwhile,the effects of second order of non-spherical gravitational perturbation on SSPS are discussed,and the variation of total energy of SSPS is also analyzed.