In studying the effects of radiation and oblateness of the primaries on the stability of collinear equilibrium points in the Robes restricted three-body problem we observed the variations of the density parameter k wi...In studying the effects of radiation and oblateness of the primaries on the stability of collinear equilibrium points in the Robes restricted three-body problem we observed the variations of the density parameter k with the mass parameter μ for constant radiation and oblateness factors on the location and stability of the collin-ear points L1, L2and L3. It is also discovered that the collinear points are unstable for k > 0 and stable for k < 0.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
To meet the increasing research demand for deep space exploration,especially for the second libration point (L2) conditional periodic orbit (Halo orbit) in the Sun-Earth system,the methods to get analytical Halo orbit...To meet the increasing research demand for deep space exploration,especially for the second libration point (L2) conditional periodic orbit (Halo orbit) in the Sun-Earth system,the methods to get analytical Halo orbit and differential-correction Halo orbit were described firstly,and the corresponding orbits accuracy was analyzed.Then,based on the results of third-order and differential-correction Halo orbits,the formation form was studied.Analysis was carried out to discuss the influence of system amplitude,initial phase,and phase difference on the formation form,as well as that of initial orbit values on form accuracy.Finally,some simulation results demonstrate the validity of the proposed methods.展开更多
This paper examines the motion of a dust grain around a triaxial primary and an oblate companion orbiting each other in elliptic orbits about their common barycenter in the neighborhood of collinear libration points. ...This paper examines the motion of a dust grain around a triaxial primary and an oblate companion orbiting each other in elliptic orbits about their common barycenter in the neighborhood of collinear libration points. The positions and stability of these points are found to be affected by the triaxiality and oblateness of the primaries, and by the semi-major axis and eccentricity of their orbits. The stability behavior of the collinear points however remains unchanged;they are unstable in the Lyapunov sense.展开更多
文摘In studying the effects of radiation and oblateness of the primaries on the stability of collinear equilibrium points in the Robes restricted three-body problem we observed the variations of the density parameter k with the mass parameter μ for constant radiation and oblateness factors on the location and stability of the collin-ear points L1, L2and L3. It is also discovered that the collinear points are unstable for k > 0 and stable for k < 0.
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.
文摘To meet the increasing research demand for deep space exploration,especially for the second libration point (L2) conditional periodic orbit (Halo orbit) in the Sun-Earth system,the methods to get analytical Halo orbit and differential-correction Halo orbit were described firstly,and the corresponding orbits accuracy was analyzed.Then,based on the results of third-order and differential-correction Halo orbits,the formation form was studied.Analysis was carried out to discuss the influence of system amplitude,initial phase,and phase difference on the formation form,as well as that of initial orbit values on form accuracy.Finally,some simulation results demonstrate the validity of the proposed methods.
文摘This paper examines the motion of a dust grain around a triaxial primary and an oblate companion orbiting each other in elliptic orbits about their common barycenter in the neighborhood of collinear libration points. The positions and stability of these points are found to be affected by the triaxiality and oblateness of the primaries, and by the semi-major axis and eccentricity of their orbits. The stability behavior of the collinear points however remains unchanged;they are unstable in the Lyapunov sense.
