We present and analyzed bi-circular restricted four-body problem model that accounts for dissipative forces. Specifically, the model for Sun–Earth–Moon-Spacecraft system is formulated with inclusion of Stokes drag and Poynting–Robertson (P–R) drag. The Lagrange points are seen to be dependent on the strength and the kind of the dissipative force involved, comparatively, the P–R drag is found to exert greater influence on the spacecraft than the Stokes drag. The linear stability analysis of the model shows that the motion of the Spacecraft around the system’s Lagrange points is stable only at $$\hbox {L}_{\mathrm {4,5}}$$ L 4 , 5 . Moreover, an examination of the dynamical behaviour of the system reveals it to be chaotic as the trajectories of the motion are exponentially divergent. This model finds great applications in the study of astronomical system and mission planning in space travels and interplanetary probes.

中文翻译：

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具有耗散力的双圆 R4BP 研究：地月聚焦视图中航天器的运动

我们提出并分析了考虑耗散力的双圆受限四体问题模型。具体来说，太阳-地球-月球-航天器系统的模型是在包含斯托克斯阻力和波印廷-罗伯逊 (P-R) 阻力的情况下制定的。拉格朗日点被认为取决于所涉及的强度和耗散力的种类，相比之下，发现 P-R 阻力比斯托克斯阻力对航天器产生更大的影响。模型的线性稳定性分析表明，航天器围绕系统拉格朗日点的运动仅在 $$\hbox {L}_{\mathrm {4,5}}$$ L 4 , 5 处稳定。此外，对系统动力学行为的检查表明它是混沌的，因为运动的轨迹呈指数发散。