This study presents dynamical equations for a variable mass fourth body, accounting for radiation from the first primary body and oblateness in the second and third primary bodies. Our findings reveal that the number and positional evolution of Lagrangian points are highly sensitive to variations in radiation, oblateness, and perturbation parameters in the uv− and uw−plane, leading to the emergence of three, eight, or ten Lagrangian points. We employ linear stability analysis, utilizing the Routh–Hurwitz stability criterion, to demonstrate the instability of these Lagrangian points under specific conditions. Additionally, we investigate geometric structures, including zero velocity curves and surfaces at varying system energies, which illustrate an expansion of the potential motion region as system energy decreases. The geometry of the Newton–Raphson basins of attraction is also influenced by changes in radiation parameters and oblateness coefficients. Furthermore, we apply the Lindstedt–Poincaré technique to derive second- and third-order periodic orbits near non-collinear Lagrangian points, revealing distinct characteristics of these orbits through numerical simulations.

中文翻译：

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具有辐射和扁圆形原色的可变质量 R4BP 的动态行为


本研究提出了质量可变的第四天体的动力学方程，考虑了来自第一初级天体的辐射以及第二和第三初级天体的扁度。我们的研究结果表明，拉格朗日点的数量和位置演化对 uv 和 uw 平面中辐射、扁度和扰动参数的变化高度敏感，导致出现 3 个、8 个或 10 个拉格朗日点。我们采用线性稳定性分析，利用 Routh-Hurwitz 稳定性准则来证明这些拉格朗日点在特定条件下的不稳定性。此外，我们还研究了几何结构，包括零速度曲线和不同系统能量下的表面，这说明了随着系统能量的降低，势能运动区域的扩展。牛顿-拉夫森引力盆地的几何形状也受到辐射参数和扁度系数变化的影响。此外，我们应用 Lindstedt-Poincaré 技术推导了非共线拉格朗日点附近的二阶和三阶周期性轨道，通过数值模拟揭示了这些轨道的不同特征。