Displaced non-Keplerian orbits above planetary bodies can be achieved by orientating the solar sail normal to the sun line. The dynamical systems techniques are employed to analyze the nonlinear dynamics of a displace...Displaced non-Keplerian orbits above planetary bodies can be achieved by orientating the solar sail normal to the sun line. The dynamical systems techniques are employed to analyze the nonlinear dynamics of a displaced orbit and different topologies of equilibria are yielded from the basic configurations of Hill＇s region, which have a saddlenode bifurcation point at the degenerated case. The solar sail near hyperbolic or degenerated equilibrium is quite unstable. Therefore, a controller preserving Hamiltonian structure is presented to stabilize the solar sail near hyperbolic or degenerated equilibrium, and to generate the stable Lissajous orbits that stay stable inside the stabilizing region of the controller. The main contribution of this paper is that the controller preserving Hamiltonian structure not only changes the instability of the equilibrium, but also makes the modified elliptic equilibrium become unique for the controlled system. The allocation law of the controller on the sail＇s attitude and lightness number is obtained, which verifies that the controller is realizable.展开更多
The present paper deals with the study of equilibrium positions of the motion of a system of two artificial satellites connected by a light, flexible, inextensible and non-conducting cable under the influence of solar...The present paper deals with the study of equilibrium positions of the motion of a system of two artificial satellites connected by a light, flexible, inextensible and non-conducting cable under the influence of solar radiation pressure, earth’s oblateness, shadow of the earth and air resistance. Here, we study the case of circular orbit of the centre of mass of the system. We derive differential equations of motion of the system. General solutions of the differential equations are beyond the reach. On the other hand, the general solutions do not serve our purpose. Jacobian integral of the system has also been obtained. Thereafter equilibrium positions of the motion of the system have been obtained.展开更多
基金supported by the National Natural Science Foundation of China (11172020)the "Vision" Foundation for Talent Assistant Professor from Ministry of Industry and Information Technologythe "Blue-Sky" Foundation for Talent Assistant Professor from Beihang University
文摘Displaced non-Keplerian orbits above planetary bodies can be achieved by orientating the solar sail normal to the sun line. The dynamical systems techniques are employed to analyze the nonlinear dynamics of a displaced orbit and different topologies of equilibria are yielded from the basic configurations of Hill＇s region, which have a saddlenode bifurcation point at the degenerated case. The solar sail near hyperbolic or degenerated equilibrium is quite unstable. Therefore, a controller preserving Hamiltonian structure is presented to stabilize the solar sail near hyperbolic or degenerated equilibrium, and to generate the stable Lissajous orbits that stay stable inside the stabilizing region of the controller. The main contribution of this paper is that the controller preserving Hamiltonian structure not only changes the instability of the equilibrium, but also makes the modified elliptic equilibrium become unique for the controlled system. The allocation law of the controller on the sail＇s attitude and lightness number is obtained, which verifies that the controller is realizable.
文摘The present paper deals with the study of equilibrium positions of the motion of a system of two artificial satellites connected by a light, flexible, inextensible and non-conducting cable under the influence of solar radiation pressure, earth’s oblateness, shadow of the earth and air resistance. Here, we study the case of circular orbit of the centre of mass of the system. We derive differential equations of motion of the system. General solutions of the differential equations are beyond the reach. On the other hand, the general solutions do not serve our purpose. Jacobian integral of the system has also been obtained. Thereafter equilibrium positions of the motion of the system have been obtained.
