<p>This study explores the dynamical behavior of an infinitesimal test particle within the perturbed Circular Restricted Three-Body Problem (CR3BP). The model incorporates a triaxial radiating larger primary and a smaller primary influenced by modified gravity. By analyzing the linearized equations of motion near the equilibrium points, we characterize the periodic solutions and demonstrate that perturbations significantly alter the orbital periods and overall system dynamics. Furthermore, the impact of perturbations on the linear stability, critical mass parameters, and the existence of tadpole orbits associated with the non-collinear equilibrium points <InlineEquation ID="IEq1"> <EquationSource Format="TEX">$L_{4,5}$</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>L</mi> <mrow> <mn>4</mn> <mo>,</mo> <mn>5</mn> </mrow> </msub> </math></EquationSource> </InlineEquation> is investigated. In addition, first-order analytical periodic solutions around the collinear equilibrium points <InlineEquation ID="IEq2"> <EquationSource Format="TEX">$L_{1,2,3}$</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>L</mi> <mrow> <mn>1</mn> <mo>,</mo> <mn>2</mn> <mo>,</mo> <mn>3</mn> </mrow> </msub> </math></EquationSource> </InlineEquation> are evaluated. Planar Lyapunov orbits around the collinear points <InlineEquation ID="IEq3"> <EquationSource Format="TEX">$L_1$</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>L</mi> <mn>1</mn> </msub> </math></EquationSource> </InlineEquation> and <InlineEquation ID="IEq4"> <EquationSource Format="TEX">$L_2$</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>L</mi> <mn>2</mn> </msub> </math></EquationSource> </InlineEquation> are constructed utilizing the state transition matrix alongside pseudo-arclength continuation methods, extending solutions beyond the scope of linear approximations. The stability of these trajectories is thoroughly evaluated via the monodromy matrix, revealing insights into their unstable nature and the impact of parameters such as the modified gravity term.</p>

Motion around the equilibrium points in the perturbed restricted three body problem with modified gravity

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发表日期：

2026年5月26日

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Ravi Kumar Verma,
Sergey Ershkov,
Saleem Yousuf,
Elbaz I. Abouelmagd

摘要

This study explores the dynamical behavior of an infinitesimal test particle within the perturbed Circular Restricted Three-Body Problem (CR3BP). The model incorporates a triaxial radiating larger primary and a smaller primary influenced by modified gravity. By analyzing the linearized equations of motion near the equilibrium points, we characterize the periodic solutions and demonstrate that perturbations significantly alter the orbital periods and overall system dynamics. Furthermore, the impact of perturbations on the linear stability, critical mass parameters, and the existence of tadpole orbits associated with the non-collinear equilibrium points $L_{4,5}$ $L_{4, 5}$ is investigated. In addition, first-order analytical periodic solutions around the collinear equilibrium points $L_{1,2,3}$ $L_{1, 2, 3}$ are evaluated. Planar Lyapunov orbits around the collinear points $L_1$ $L_{1}$ and $L_2$ $L_{2}$ are constructed utilizing the state transition matrix alongside pseudo-arclength continuation methods, extending solutions beyond the scope of linear approximations. The stability of these trajectories is thoroughly evaluated via the monodromy matrix, revealing insights into their unstable nature and the impact of parameters such as the modified gravity term.