非线性条件下编队卫星周期性相对运动条件

利用编队卫星机械能守恒原理，提出了非线性条件下求解编队卫星周期性相对运动条件的新方法，给出了非线性周期相对运动的初始条件。编队卫星相对距离较近时，利用非线性周期运动条件，可修正Hill方程的初始条件，抑制编队卫星的长期漂移。编队卫星相对距离较大，非线性因素不可忽略时，利用非线性周期运动条件，可找到不需消耗任何燃料的周期性相对运动轨道。最后的数值仿真结果验证了该方法的正确性。

Periodic Relative Motion Condition for Satellites Formations Considering Nonlinearity

Presented was a new method to design the periodic relative rotating orbits for satellites formations using the law of energy conservation and find analytic solutions of the initial conditions for the nonlinearity relative motion equations. When the relative range of formation was small, the secular growth errors of Hill equations solutions were eliminated with nonlinearity initial condition corrected. When the relative range was large and the effects of nonlinearity could not be neglected, the nonlinearity periodic relative rotating orbits could be found using the nonlinearity initial conditions. The numerical simulations demonstrated the effectiveness of the new approach and analytic solutions.