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Homoclinic and heteroclinic solutions of cubic strongly nonlinear autonomous oscillators by hyperbolic lindstedt-poincaré method

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中国科学:技术科学 2010年第2期 216-216页

作者： SZE Kam Yim Department of Mechanical Engineering The University of Hong Kong

The hyperbolic lindstedt-poincaré method is applied to determine the homoclinic and heteroclinic solutions of cubic strongly nonlinear oscillators of the form  + cx + cx=ε f （ μ, x, ）.In the method, the hyperbolic functions are employed instead of the periodic functions in the lindstedt-poincaré procedure. Critical value of parameter μ under which there exists homoclinic or heteroclinic orbit can be determined by the perturbation procedure. Typical applications are studied in detail. To illustrate the accuracy of the present method, its predictions are compared with those of Runge-Kutta method.

关键词： lindstedt-poincaré method nonlinear autonomous oscillator homoclinic orbit heteroclinic orbit

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Halo Orbits around Sun-Earth L1 in Photogravitational Restricted Three-Body Problem with Oblateness of Smaller Primary

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International Journal of Astronomy and Astrophysics 2016年第3期6卷 293-311页

作者： Prithiviraj Chidambararaj Ram Krishan Sharma Department of Aerospace Engineering Karunya University Coimbatore India

This paper deals with generation of halo orbits in the three-dimensional photogravitational restricted three-body problem, where the more massive primary is considered as the source of radiation and the smaller primary is an oblate spheroid with its equatorial plane coincident with the plane of motion. Both the terms due to oblateness of the smaller primary are considered. Numerical as well as analytical solutions are obtained around the Lagrangian point L1, which lies between the primaries, of the Sun-Earth system. A comparison with the real time flight data of SOHO mission is made. Inclusion of oblateness of the smaller primary can improve the accuracy. Due to the effect of radiation pressure and oblateness, the size and the orbital period of the halo orbit around L1 are found to increase.

关键词： Halo Orbits Photogravitational Restricted Three-Body Problem Oblateness lindstedt-poincaré method Lagrangian Point SOHO

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