Compact normalisations in the elliptic restricted three body problem
Compact normalisations in the elliptic restricted three body problem
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DOI：
10.1007/s10509-017-3195-8
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发表时间：
2017-10
影响因子：
1.9
通讯作者：
J. Palacián;Jasson Vanegas;P. Yanguas
中科院分区：
文献类型：
--
作者：
J. Palacián;Jasson Vanegas;P. Yanguas
本文考虑了空间椭圆型限制性三体问题中质量可忽略的质点绕其中一个质点旋转的情形。该系统是在惯性系中建模的，通过一个哈密顿函数表示一个非自治的动力系统，具有三个自由度，周期性地依赖于时间。应用三个一阶Lie变换，依次消除了无穷小粒子运动的平均反常、系统的时间依赖性和质量可忽略粒子的节点幅角。所有的变换都以紧凑的方式实现，即通过无穷级数进行计算。这种方法对于处理某些人造卫星问题是非常有用的，或者一般来说，对于无穷小粒子到其轨道周围物体的距离与两个主粒子之间的距离之比小于1但接近1的系统，在这种情况下，势的Legendre展开收敛缓慢，并且必须考虑级数的许多项。
This paper considers the spatial elliptic restricted three body problem in the case that the particle with negligible mass is revolving around one of the primaries. The system is modelled in an inertial frame through a Hamiltonian function representing a non-autonomous dynamical system with three degrees of freedom that depends periodically on time. Three Lie transformations are applied at first order to eliminate successively the mean anomaly of the infinitesimal particle’s motion, the time dependence of the system and the argument of the node of the particle with negligible mass. All the transformations are implemented in a compact way, that is, carrying out the computations by means of infinite series. This approach can be very useful to deal with certain artificial satellite problems or, in general, with systems such that the ratio between the distance of the infinitesimal particle to the body around it orbits and the distance between the two primaries is smaller than one but close to it. In this case the Legendre expansion of the potential converges slowly and many terms of the series must be taken into consideration.