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Effect of variation of charge in the circular restricted three-body problem with variable masses

机译:可变质量的圆形受限三体问题中电荷变化的影响

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In the present paper, we are concerned by some investigation on circular restricted threebodyproblem (CR3BP), where we assume that the primaries have variable masses and variablecharges. Among the principal tools used in the present study, we cite the well known Meshcherskiitransformation. We have derived the equations of motion and Jacobi integral which differby variation constant k and charge q from the classical restricted three-body problem. Moreexactly, in this paper, we have drawn the equilibrium points, the zero-velocity curves, the periodicorbits, the surfaces and the basins of attraction for the different values of charge. We have foundone equilibrium point when the charge is q = 0.4 and three equilibrium points when its value isq = 0.501. We also have drawn the periodic orbits for these two values of charge and found thatthey are periodic. We have also plotted the zero-velocity surfaces for these two values of chargesand found a tremendous variation in these two surfaces. We notice that the Poincaré surfaces ofsection are shifting away from the origin, when we increase the value of charge. We also got differentsurfaces for the motion of infinitesimal body, with respect to the variations of charge. Thebasins of attraction have been drawn for these two values of charge by using Newton-Raphsoniterative method. We also noticed that by increasing the values of charge, the basins of attractionare shrinking. For the stability of the equilibrium points that we have studied, we found that,among them, one is stable and three others are unstable.
机译:在本文中,我们对圆形受限三体问题(CR3BP)进行了一些研究,其中我们假定原色具有可变的质量和可变的电荷。在本研究中使用的主要工具中,我们引用了众所周知的Meshcherskii变换。我们从经典的受限三体问题中得出了运动方程和雅可比积分方程,它们的变化常数为k,电荷为q。更确切地说,在本文中,我们针对不同的电荷值绘制了平衡点,零速度曲线,周期轨道,表面和吸引池。当电荷为q = 0.4时,我们找到了一个平衡点;当电荷值为q = 0.501时,我们找到了三个平衡点。我们还绘制了这两个电荷值的周期轨道,发现它们是周期的。我们还绘制了这两个电荷值的零速度表面,并发现这两个表面有巨大的变化。我们注意到,当我们增加电荷的值时,截面的庞加莱曲面正偏离原点。关于电荷的变化,我们也得到了无限小物体运动的不同表面。通过使用牛顿-拉格尼特方法对这两个电荷值绘制了吸引流域。我们还注意到,通过增加电荷的值,吸引盆地正在缩小。对于我们研究的平衡点的稳定性,我们发现其中一个是稳定的,另外三个是不稳定的。

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