论文部分内容阅读
针对三体问题周期轨道计算方法存在计算量大、改变雅可比能量和局限于计算特定周期轨道等不足,本文提出了一种计算周期轨道的新方法。首先建立了一种初始点和投影点关系的改进型庞加莱截面图,能够更直观地反映随着初始点改变周期轨道的演变和分叉;其次基于改进的庞加莱截面图,通过初始点与投影点的对应关系筛选出可能存在周期轨道的候选区间;然后在该候选区间内利用状态转移矩阵给出距离周期轨道初始点真实解非常接近的初始猜想;最后采用打靶法求解能够快速得到周期轨道的数值解。本文方法不需要改变三体系统的雅可比能量,迭代次数少,能够快速计算得到大范围、具有x轴对称性的周期轨道。以地月圆形限制性三体问题为例进行仿真,验证了该方法的快速性和有效性。
Aiming at the shortcomings of three-body periodic orbit calculation methods, such as large amount of calculation, changing Jacobian energy and being limited to calculating a specific periodic orbit, a new method for calculating periodic orbits is proposed. Firstly, an improved Poincaré cross section diagram of initial point and projection point is established, which can more directly reflect the evolution and bifurcation of the periodic orbit with the initial point. Secondly, based on the modified Poincaré section, And the corresponding points of the projection points are screened out candidate intervals that may have periodic orbits; then the state transition matrix is used to give the initial guess which is very close to the true solution of the initial point of the periodic orbit; finally, the shooting method can be used to quickly obtain Numerical solution of periodic orbits. This method does not need to change the Jacobian energy of the three-body system, and has fewer iterations. It can quickly calculate the large-scale periodic orbits with x-axis symmetry. Taking the earth-moon circular restricted three-body problem as an example, the simulation shows that the method is rapid and effective.