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The Sitnikov problem investigation with the method of multiple scales

Dehghan Manshadi, A ; Sharif University of Technology | 2018

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  1. Type of Document: Article
  2. DOI: 10.1007/s40995-017-0180-6
  3. Publisher: Springer International Publishing , 2018
  4. Abstract:
  5. The method of multiple scales is one of the common perturbation techniques for exploring nonlinear ordinary differential equations. Sitnikov has presented a mathematics model of a negligible mass body oscillation perpendicular to a plane in which two heavy bodies with equal mass orbit on itself Keplerian ellipse. This problem is well known as the Sitnikov problem. In this investigation, the method of multiple scales is applied to the Sitnikov problem and it presented an analytical response that is consistent with numerical solution. At first step, the circular form of the Sitnikov equation is approximated by MMS and then the obtained dynamic model from first step is employed to investigate the elliptical form of the Sitnikov equation. Some initial conditions and eccentricities of the primary bodies are studied and results are compared with numerical solution. Results show that estimated analytical solution can help to discover the Sitnikov equation behavior. © 2017, Shiraz University
  6. Keywords:
  7. Perturbation technique ; Sitnikov equation ; The Method of Multiple Scales
  8. Source: Iranian Journal of Science and Technology, Transaction A: Science ; Volume 42, Issue 3 , 2018 , Pages 1471-1477 ; 10286276 (ISSN)
  9. URL: https://link.springer.com/article/10.1007/s40995-017-0180-6