带Poynting-Robertson阻力的广义光引力限制三体问题的二阶正规化
Second Order Normalization in the Generalized Photogravitational Restricted Three Body Problem with Poynting-Robertson Drag
摘要：
本文对带Poynting-Robertson阻力的广义光引力限制三体问题进行了二阶归一化。我们已经执行了Birkhoff的正规化的哈密顿量。为此，我们利用Henrard的方法，并扩大了双达朗贝尔系列的第三个机构的坐标。我们已经找到了一阶和二阶分量的值。二阶分量作为两个偏微分方程的解而得到。我们利用KAM定理的第一个条件来求解这些方程。一阶和二阶分量受辐射压、扁率和P-R阻力的影响。最后得到了哈密顿量在$I_1^{1/2}I_2^{1/2}$零点处的三阶部分$H_3$。
英文摘要：
In this paper we have performed second order normalization in the generalised photogravitaional restricted three body problem with Poynting-Robertson drag. We have performed Birkhoff's normalization of the Hamiltonian. For this we have utilised Henrard's method and expanded the coordinates of the third body in Double d'Alembert series. We have found the values of first and second order components. The second order components are obtained as solutions of the two partial differential equations. We have employed the first condition of KAM theorem in solving these equations. The first and second order components are affected by radiation pressure, oblateness and P-R drag. Finaly we obtained the third order part $H_3$ of the Hamiltonian in $I_1^{1/2}I_2^{1/2}$ zero.
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