Significant propellant mass saving can be obtained with the use of complex multiple intermediate flyby maneuvers for conventional propulsion systems,and trip time also decreases for a portion of the proper solar sail ...Significant propellant mass saving can be obtained with the use of complex multiple intermediate flyby maneuvers for conventional propulsion systems,and trip time also decreases for a portion of the proper solar sail missions.This paper discusses the performance of gravity assist(GA)in the time-optimal control problem of solar sailing with respect to sail lightness number and the energy difference between the initial and final orbit in the rendezvous problem in a two-body model,in which the GA is modeled as a substantial change in the velocity of the sailcraft at the GA time.In addition,this paper presents a method to solve the time-optimal problem of solar sailing with GA in a full ephemeris model,which introduces the third body’s gravity in a dynamic equation.This study builds a set of inner constraints that can describe the GA process accurately.Finally,this study presents an example for evaluating the accuracy and rationality of the two-body model’s simplification of GA by comparison with the full ephemeris model.展开更多
Low thrust propulsion and gravity assist (GA) are among the most promising techniques for deep space explorations.In this paper the two techniques are combined and treated comprehensively,both on modeling and numerica...Low thrust propulsion and gravity assist (GA) are among the most promising techniques for deep space explorations.In this paper the two techniques are combined and treated comprehensively,both on modeling and numerical techniques.Fuel optimal orbit rendezvous via multiple GA is first formulated as optimal guidance with multiple interior constraints and then the optimal necessary conditions,various transversality conditions and stationary conditions are derived by Pontryagin's Maximum Principle (PMP).Finally the initial orbit rendezvous problem is transformed into a multiple point boundary value problem (MPBVP).Homotopic technique combined with random searching globally and Particle Swarm Optimization (PSO),is adopted to handle the numerical difficulty in solving the above MPBVP by single shooting method.Two scenarios in the end show the merits of the present approach.展开更多
In our context,the planetary many-body problem consists of studying the motion of(n+1)-bodies under the mutual attraction of gravitation,where n planets move around a massive central body,the Sun.We establish the exis...In our context,the planetary many-body problem consists of studying the motion of(n+1)-bodies under the mutual attraction of gravitation,where n planets move around a massive central body,the Sun.We establish the existence of real analytic lower dimensional elliptic invariant tori with intermediate dimension N lies between n and 3n-1 for the spatial planetary many-body problem.Based on a degenerate KolmogorovArnold-Moser(abbr.KAM)theorem proved by Bambusi et al.(2011),Berti and Biasco(2011),we manage to handle the difficulties caused by the degeneracy of this real analytic system.展开更多
文摘Significant propellant mass saving can be obtained with the use of complex multiple intermediate flyby maneuvers for conventional propulsion systems,and trip time also decreases for a portion of the proper solar sail missions.This paper discusses the performance of gravity assist(GA)in the time-optimal control problem of solar sailing with respect to sail lightness number and the energy difference between the initial and final orbit in the rendezvous problem in a two-body model,in which the GA is modeled as a substantial change in the velocity of the sailcraft at the GA time.In addition,this paper presents a method to solve the time-optimal problem of solar sailing with GA in a full ephemeris model,which introduces the third body’s gravity in a dynamic equation.This study builds a set of inner constraints that can describe the GA process accurately.Finally,this study presents an example for evaluating the accuracy and rationality of the two-body model’s simplification of GA by comparison with the full ephemeris model.
基金supported by the National Natural Science Foundation of China(Grant Nos. 10832004 and 11072122)
文摘Low thrust propulsion and gravity assist (GA) are among the most promising techniques for deep space explorations.In this paper the two techniques are combined and treated comprehensively,both on modeling and numerical techniques.Fuel optimal orbit rendezvous via multiple GA is first formulated as optimal guidance with multiple interior constraints and then the optimal necessary conditions,various transversality conditions and stationary conditions are derived by Pontryagin's Maximum Principle (PMP).Finally the initial orbit rendezvous problem is transformed into a multiple point boundary value problem (MPBVP).Homotopic technique combined with random searching globally and Particle Swarm Optimization (PSO),is adopted to handle the numerical difficulty in solving the above MPBVP by single shooting method.Two scenarios in the end show the merits of the present approach.
文摘In our context,the planetary many-body problem consists of studying the motion of(n+1)-bodies under the mutual attraction of gravitation,where n planets move around a massive central body,the Sun.We establish the existence of real analytic lower dimensional elliptic invariant tori with intermediate dimension N lies between n and 3n-1 for the spatial planetary many-body problem.Based on a degenerate KolmogorovArnold-Moser(abbr.KAM)theorem proved by Bambusi et al.(2011),Berti and Biasco(2011),we manage to handle the difficulties caused by the degeneracy of this real analytic system.
