A new method is developed for stabilizing motion on collinear libration point orbits using the formalism of the circular restricted three body problem. Linearization about the collinear libration point orbits yields a...A new method is developed for stabilizing motion on collinear libration point orbits using the formalism of the circular restricted three body problem. Linearization about the collinear libration point orbits yields an unstable linear parameter-varying system with periodic coefficients. Given the variational equations, an innovative control law based on characteristic exponent assignment is introduced for libration point orbit maintenance. A numerical simulation choosing the Richardson＇s third order approximation for a halo orbit as a nominal orbit is conducted, and the results demonstrate the effectiveness of this control law.展开更多
In this paper we study the characteristic exponents of periodic system x' +p(t)x' + q(t)x = 0. In the case when q(t) ≠ 0 and we obtain someresults which generalize the corresponding results of the autonomous...In this paper we study the characteristic exponents of periodic system x' +p(t)x' + q(t)x = 0. In the case when q(t) ≠ 0 and we obtain someresults which generalize the corresponding results of the autonomous systemx' + px' + qx = 0.展开更多
In this paper, a second order linear differential equation is considered, and an accurate estimate method of characteristic exponent for it is presented. Finally, we give some examples to verify the feasibility of our...In this paper, a second order linear differential equation is considered, and an accurate estimate method of characteristic exponent for it is presented. Finally, we give some examples to verify the feasibility of our result.展开更多
In this paper we shall give a simple and easy method to estimate the characteristic exponents for a class of second order linear different equation with periodic coefficient which frequently occurs in application.
Parametric resonance can lead to dangerously large rolling motions, endangering the ship, cargo and crew. The QR-faetorization method for calculating （LCEs） Lyapunov Characteristic Exponents was introduced; parametr...Parametric resonance can lead to dangerously large rolling motions, endangering the ship, cargo and crew. The QR-faetorization method for calculating （LCEs） Lyapunov Characteristic Exponents was introduced; parametric resonance stability of ships in longitudinal waves was then analyzed using LCEs. Then the safe and unsafe regions of target ships were then identified. The results showed that this method can be used to analyze ship stability and to accurately identify safe and unsafe operating conditions for a ship in longitudinal waves.展开更多
In this paper,we present a study on the impact of radiation pressure and circumstellar dust on the motion of a test particle in the framework of the restricted four-body problem under the Manev’s field.We show that t...In this paper,we present a study on the impact of radiation pressure and circumstellar dust on the motion of a test particle in the framework of the restricted four-body problem under the Manev’s field.We show that the distribution of equilibrium points on the plane of motion is slightly different from that of the classical Newtonian problem.With the aid of the Lyapunov characteristic exponents,we show that the system is sensitive to changes in initial conditions;hence,the orbit of the system is found to be chaotic in the phase space for the given initial conditions.Furthermore,a numerical application of this model to a stellar system(Gliese 667C)is considered,which validates the dependence of the equilibrium points on the mass parameter.We show that the non-collinear equilibrium points of this stellar system are distributed symmetrically about the x-axis,and five of them are linearly stable.The basins of attraction of the system show that the equilibrium points have irregular boundaries,and we use the energy integral and the Manev parameter to illustrate the zero-velocity curves showing the permissible region of motion of the test particle with respect to the Jacobi constant.展开更多
基金supported by the National Natural Science Foundation of China(10702003)
文摘A new method is developed for stabilizing motion on collinear libration point orbits using the formalism of the circular restricted three body problem. Linearization about the collinear libration point orbits yields an unstable linear parameter-varying system with periodic coefficients. Given the variational equations, an innovative control law based on characteristic exponent assignment is introduced for libration point orbit maintenance. A numerical simulation choosing the Richardson＇s third order approximation for a halo orbit as a nominal orbit is conducted, and the results demonstrate the effectiveness of this control law.
文摘In this paper we study the characteristic exponents of periodic system x' +p(t)x' + q(t)x = 0. In the case when q(t) ≠ 0 and we obtain someresults which generalize the corresponding results of the autonomous systemx' + px' + qx = 0.
基金supported by Foundation of Fujian Education Committee (JA08012)
文摘In this paper, a second order linear differential equation is considered, and an accurate estimate method of characteristic exponent for it is presented. Finally, we give some examples to verify the feasibility of our result.
基金Supported by Research Foundation of the Fujian Education Bureau (JA04158)the Natural Science Foundation of Fujian Province (No.2006J0209)the Foundation of Developing Science and Technology of Fuzhou University under the grant (2005-XQ-20).
文摘In this paper we shall give a simple and easy method to estimate the characteristic exponents for a class of second order linear different equation with periodic coefficient which frequently occurs in application.
文摘Parametric resonance can lead to dangerously large rolling motions, endangering the ship, cargo and crew. The QR-faetorization method for calculating （LCEs） Lyapunov Characteristic Exponents was introduced; parametric resonance stability of ships in longitudinal waves was then analyzed using LCEs. Then the safe and unsafe regions of target ships were then identified. The results showed that this method can be used to analyze ship stability and to accurately identify safe and unsafe operating conditions for a ship in longitudinal waves.
文摘In this paper,we present a study on the impact of radiation pressure and circumstellar dust on the motion of a test particle in the framework of the restricted four-body problem under the Manev’s field.We show that the distribution of equilibrium points on the plane of motion is slightly different from that of the classical Newtonian problem.With the aid of the Lyapunov characteristic exponents,we show that the system is sensitive to changes in initial conditions;hence,the orbit of the system is found to be chaotic in the phase space for the given initial conditions.Furthermore,a numerical application of this model to a stellar system(Gliese 667C)is considered,which validates the dependence of the equilibrium points on the mass parameter.We show that the non-collinear equilibrium points of this stellar system are distributed symmetrically about the x-axis,and five of them are linearly stable.The basins of attraction of the system show that the equilibrium points have irregular boundaries,and we use the energy integral and the Manev parameter to illustrate the zero-velocity curves showing the permissible region of motion of the test particle with respect to the Jacobi constant.
