In this paper, we present a new approach for solving equations of motion for the trapped motion of the infinitesimal mass m in case of the elliptic restricted problem of three bodies (ER3BP) (primaries \(M_\mathrm{Sun}\) and \(m_\mathrm{planet}\) are rotating around their common centre of masses on elliptic orbit): a new type of the solving procedure is implemented here for solving equations of motion of the infinitesimal mass m in the vicinity of the barycenter of masses \(M_\mathrm{Sun}\) and \(m_\mathrm{planet}\). Meanwhile, the system of equations of motion has been successfully explored with respect to the existence of analytical way for presentation of the approximated solution. As the main result, equations of motion are reduced to the system of three nonlinear ordinary differential equations: (1) equation for coordinate x is proved to be a kind of appropriate equation for the forced oscillations during a long-time period of quasi-oscillations (with a proper restriction to the mass \(m_\mathrm{planet}\)), (2) equation for coordinate y reveals that motion is not stable with respect to this coordinate and condition \(y \sim 0\) would be valid if only we choose zero initial conditions, and (3) equation for coordinate z is proved to be Riccati ODE of the first kind. Thus, infinitesimal mass m should escape from vicinity of common centre of masses \(M_\mathrm{Sun}\) and \(m_\mathrm{planet}\) as soon as the true anomaly f increases insofar. The main aim of the current research is to point out a clear formulation of solving algorithm or semi-analytical procedure with partial cases of solutions to the system of equations under consideration. Here, semi-analytical solution should be treated as numerical algorithm for a system of ordinary differential equations (ER3BP) with well-known code for solving to be presented in the final form.

在本文中，我们提出了一种新的方法来解决运动方程为被困运动的无穷小的质量米三个机构的椭圆型限制性问题（ER3BP）（初选的情况下\（M_ \ mathrm {孙} \）和\ （m_ \ mathrm {planet} \）绕其在椭圆轨道上的共同质量中心旋转）：此处采用一种新型求解程序，用于求解质量重心附近的无穷小质量m的运动方程\（M_ \ mathrm {Sun} \）和\（m_ \ mathrm {planet} \）。同时，已经成功地探索了运动方程组，其中存在解析方法来表示近似解。作为主要的结果是，运动方程被减少到三个非线性常微分方程的系统：（1）方程坐标X被证明是一种用于用适当的方程式的强迫振荡期间的经过较长时间的期间的准振荡（对质量\（m_ \ mathrm {planet} \）有适当的限制），（2）坐标y的方程式表明，相对于该坐标和条件\（y \ sim 0 \），运动不稳定如果仅选择零个初始条件，则将是有效的，并且（3）坐标z的等式被证明是第一类Riccati ODE。因此，无穷小质量m应该在真正异常f尽快从共同的质量中心\（M_ \ mathrm {Sun} \）和\（m_ \ mathrm {planet} \）附近逃逸。就此增加。当前研究的主要目的是指出一种明确的求解算法或半解析过程公式，其中包括正在考虑的方程组解的部分情况。在这里，应将半解析解作为常微分方程组（ER3BP）的数值算法，并使用最终求解的众所周知代码进行求解。