A Modified Restricted Three-Body Model with a Rotating Mass Dipole and Triaxial Secondary
DOI:
https://doi.org/10.62054/ijdm/0303.10Abstract
This study presents a modified restricted three-body model that incorporates a rotating mass dipole primary and a triaxial secondary to provide a more general description of motion in irregular binary celestial systems. The classical restricted three-body framework is extended by introducing the dipole half-separation, force-ratio parameter, and two triaxiality parameters associated with the non-spherical secondary. The governing equations of motion are formulated in a uniformly rotating coordinate system, and the corresponding effective potential is derived. From the proposed formulation, the mean motion and Jacobi integral are obtained, providing the fundamental dynamical relations required for studying the motion of the infinitesimal body. The formulation also accounts for the combined influence of the asymmetric mass distribution of the dipole primary and the geometric deformation of the secondary. Appropriate limiting cases are considered to demonstrate the consistency of the model with established restricted three-body formulations when the additional perturbing parameters vanish. The resulting framework provides a unified mathematical model for investigating the dynamics of test particles in binary systems involving irregular and non-spherical primary bodies.
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