# Reduction the secular solution to periodic solution in the generalized restricted three-body problem

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## Abstract

The aim of the present work is to find the secular solution around the triangular equilibrium points and reduce it to the periodic solution in the frame work of the generalized restricted thee-body problem. This model is generalized in sense that both the primaries are oblate and radiating as well as the gravitational potential from a belt. We show that the linearized equation of motion of the infinitesimal body around the triangular equilibrium points has a secular solution when the value of mass ratio equals the critical mass value. Moreover, we reduce this solution to periodic solution, as well as some numerical and graphical investigations for the effects of the perturbed forces are introduced. This model can be used to examine the existence of a dust particle near the triangular points of an oblate and radiating binary stars system surrounded by a belt.

## Keywords

Restricted three-body problem Secular and periodic solutions Oblateness coefficients Radiation pressure Potential from the belt## Notes

### Acknowledgements

The authors (especially the first author) wish to express their gratitude to referees for their useful suggestions and criticism which improved the presentation of the paper.

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