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

机译:圆形受限制的三体问题中电荷变化的影响

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摘要

In the present paper, we are concerned by some investigation on circular restricted three-body problem (CR3BP), where we assume that the primaries have variable masses and variable charges. Among the principal tools used in the present study, we cite the well known Meshcherskii transformation. We have derived the equations of motion and Jacobi integral which differ by variation constant k and charge q from the classical restricted three-body problem. More exactly, in this paper, we have drawn the equilibrium points, the zero-velocity curves, the periodic orbits, the surfaces and the basins of attraction for the different values of charge. We have found one equilibrium point when the charge is q=0.4 and three equilibrium points when its value is q=0.501. We also have drawn the periodic orbits for these two values of charge and found that they are periodic. We have also plotted the zero-velocity surfaces for these two values of charges and found a tremendous variation in these two surfaces. We notice that the Poincaré surfaces of section are shifting away from the origin, when we increase the value of charge. We also got different surfaces for the motion of infinitesimal body, with respect to the variations of charge. The basins of attraction have been drawn for these two values of charge by using Newton-Raphson iterative method. We also noticed that by increasing the values of charge, the basins of attraction are 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,我们对循环限制的三体问题(CR3BP)进行了一些调查,我们假设初选具有可变质量和可变费用。在本研究中使用的主要工具中,我们引用了众所周知的Meshcherskii转换。我们已经衍生出运动和雅各的方程,其与常量常数k不同的变化,从经典限制的三体问题中充电q。更确切地说,在本文中,我们已经绘制了均衡点,零速度曲线,周期性轨道,表面和吸引力的盆地,用于不同的电荷值。当电荷为Q = 0.4时,我们发现了一个平衡点,当其值为Q = 0.501时,Q = 0.4和三个平衡点。我们还为这两个充电值绘制了周期性轨道,并发现它们是周期性的。我们还绘制了这两个电荷值的零速度表面,并发现这两个表面的巨大变化。我们注意到,当我们增加电荷价值时,部分部分的剖面曲面正在远离起源。对于电荷变化,我们还获得了无限的身体运动的不同表面。通过使用Newton-Raphson迭代方法,已经为这两个充电值绘制了吸引力的盆地。我们还注意到,通过增加电荷价值,吸引力的盆地正在缩小。对于我们研究的均衡点的稳定性,我们发现,其中,一个是稳定的,三个其他不稳定。

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