In this paper, we use Port-Hamiltonian framework to stabilize the Lagrange <span style="font-family:Verdana;">points in the Sun-Earth three-dimensional Circular Restricted Three-Body Problem (CRTBP). T...In this paper, we use Port-Hamiltonian framework to stabilize the Lagrange <span style="font-family:Verdana;">points in the Sun-Earth three-dimensional Circular Restricted Three-Body Problem (CRTBP). Through rewriting the CRTBP into Port-Hamiltonian framework, we are allowed to design the feedback controller through ener</span><span style="font-family:Verdana;">gy-shaping and dissipation injection. The closed-loop Hamiltonian is </span><span style="font-family:Verdana;">a candidate of the Lyapunov function to establish nonlinear stability of the designed equilibrium, which enlarges the application region of feedback controller compared with that based on linearized dynamics. Results show that th</span><span style="font-family:Verdana;">e Port-Hamiltonian</span><span style="font-family:Verdana;"> a</span><span style="font-family:Verdana;">pproach allows us to successfully stabilize the Lagrange points, where the Linear Quadratic Regulator (LQR) may fail. The feedback </span><span style="font-family:Verdana;">system based on Port-Hamiltonian approach is also robust against whit</span><span style="font-family:Verdana;">e noise in the inputs.</span>展开更多
With the terms of the exact series solution taken as trial functions, the method of point collocation was used to calculate the large deflection of a circular plate. The axisymmetrical bending formulae were developed ...With the terms of the exact series solution taken as trial functions, the method of point collocation was used to calculate the large deflection of a circular plate. The axisymmetrical bending formulae were developed for the calculation of a circular plate subjected to polynomial distributed loads, a concentrated load at the center, uniform radial forces and moments along the edge or their combinations. The support may be elastic. The buckling load was calculated. Under action of uniformly distributed load, central load or their compound load, solutions were compared with those obtained by other methods. Buckling beyond critical thrust was compared with that calculated by the power series method. The method presented in this paper has advantages of wide convergent range, high precision and short computing time. Moreover, the computing time is nearly independent of the complexity of the loads.展开更多
Exact solution of the nonlinear boundary value problem for the basic equation and boundary condition of circular membrane under central force was obtained by using new simple methods. The existence and uniqueness of t...Exact solution of the nonlinear boundary value problem for the basic equation and boundary condition of circular membrane under central force was obtained by using new simple methods. The existence and uniqueness of the solution were discussed by using of modern immovable point theorems. Although specific problem is treated, the basic principles of the methods can be applied to a considerable variety of nonlinear problems.展开更多
In the framework of the circular restricted three-body problem, the center manifolds associated with collinear libration points contain all the bounded orbits moving around these points. Semianalytical computation of ...In the framework of the circular restricted three-body problem, the center manifolds associated with collinear libration points contain all the bounded orbits moving around these points. Semianalytical computation of the center manifolds and the associated canonical transformation are valuable tools for exploring the design space of libration point missions. This paper deals with the refinement of reduction to the center manifold procedure. In order to reduce the amount of calculation needed and avoid repetitive computation of the Poisson bracket, a modified method is presented. By using a polynomial optimization technique, the coordinate transformation is conducted more efficiently. In addition, an alternative way to do the canonical coordinate transformation is discussed, which complements the classical approach. Numerical simulation confirms that more accurate and efficient numerical exploration of the center manifold is made possible by using the refined method.展开更多
This paper studies Multi-modes control method for libration points formation establishment and reconfiguration.Firstly,relations between optimal impulse control and Floquet modes are investigated.Method of generating ...This paper studies Multi-modes control method for libration points formation establishment and reconfiguration.Firstly,relations between optimal impulse control and Floquet modes are investigated.Method of generating modes is proposed.Characteristics of the mode coefficients stimulated at different time are also given.Studies show that coefficients of controlled modes can be classified into four types,and formation establishment and reconfiguration can be achieved by multi-impulse control with the presented method of generating modes.Then,since libration points formation is generally unstable,mutli-modes keeping control method which can stabilize five Floquet modes simultaneously is proposed.Finally,simulation on formation establishment and reconfiguration are carried out by using method of generating modes and mutli-modes keeping control method.Results show that the proposed control method is effective and practical.展开更多
文摘In this paper, we use Port-Hamiltonian framework to stabilize the Lagrange <span style="font-family:Verdana;">points in the Sun-Earth three-dimensional Circular Restricted Three-Body Problem (CRTBP). Through rewriting the CRTBP into Port-Hamiltonian framework, we are allowed to design the feedback controller through ener</span><span style="font-family:Verdana;">gy-shaping and dissipation injection. The closed-loop Hamiltonian is </span><span style="font-family:Verdana;">a candidate of the Lyapunov function to establish nonlinear stability of the designed equilibrium, which enlarges the application region of feedback controller compared with that based on linearized dynamics. Results show that th</span><span style="font-family:Verdana;">e Port-Hamiltonian</span><span style="font-family:Verdana;"> a</span><span style="font-family:Verdana;">pproach allows us to successfully stabilize the Lagrange points, where the Linear Quadratic Regulator (LQR) may fail. The feedback </span><span style="font-family:Verdana;">system based on Port-Hamiltonian approach is also robust against whit</span><span style="font-family:Verdana;">e noise in the inputs.</span>
文摘With the terms of the exact series solution taken as trial functions, the method of point collocation was used to calculate the large deflection of a circular plate. The axisymmetrical bending formulae were developed for the calculation of a circular plate subjected to polynomial distributed loads, a concentrated load at the center, uniform radial forces and moments along the edge or their combinations. The support may be elastic. The buckling load was calculated. Under action of uniformly distributed load, central load or their compound load, solutions were compared with those obtained by other methods. Buckling beyond critical thrust was compared with that calculated by the power series method. The method presented in this paper has advantages of wide convergent range, high precision and short computing time. Moreover, the computing time is nearly independent of the complexity of the loads.
文摘Exact solution of the nonlinear boundary value problem for the basic equation and boundary condition of circular membrane under central force was obtained by using new simple methods. The existence and uniqueness of the solution were discussed by using of modern immovable point theorems. Although specific problem is treated, the basic principles of the methods can be applied to a considerable variety of nonlinear problems.
基金supported by the National Natural Science Foundation of China (Grant Nos. 11403013 and 11672126)the Fundamental Research Funds for the Central Universities (Nos. 56XAA14093 and 56YAH12036)the Postdoctoral Foundation of Jiangsu Province (No. 1301029B)
文摘In the framework of the circular restricted three-body problem, the center manifolds associated with collinear libration points contain all the bounded orbits moving around these points. Semianalytical computation of the center manifolds and the associated canonical transformation are valuable tools for exploring the design space of libration point missions. This paper deals with the refinement of reduction to the center manifold procedure. In order to reduce the amount of calculation needed and avoid repetitive computation of the Poisson bracket, a modified method is presented. By using a polynomial optimization technique, the coordinate transformation is conducted more efficiently. In addition, an alternative way to do the canonical coordinate transformation is discussed, which complements the classical approach. Numerical simulation confirms that more accurate and efficient numerical exploration of the center manifold is made possible by using the refined method.
基金supported by the National Natural Science Foundation of China(10702078)the Advance Research Program of National University of Defense Technology (JC08-01-05)
文摘This paper studies Multi-modes control method for libration points formation establishment and reconfiguration.Firstly,relations between optimal impulse control and Floquet modes are investigated.Method of generating modes is proposed.Characteristics of the mode coefficients stimulated at different time are also given.Studies show that coefficients of controlled modes can be classified into four types,and formation establishment and reconfiguration can be achieved by multi-impulse control with the presented method of generating modes.Then,since libration points formation is generally unstable,mutli-modes keeping control method which can stabilize five Floquet modes simultaneously is proposed.Finally,simulation on formation establishment and reconfiguration are carried out by using method of generating modes and mutli-modes keeping control method.Results show that the proposed control method is effective and practical.
基金Supported by the National Natural Science Foundation of China under Grant Nos.6007500460033010+1 种基金69975021 (国家自然科学基金) the National Grand Fundamental Research 973 Program of China under Grant No.G1998030502 (国家重点基础研究发展规划(973))
