Regular and Chaotic Solutions of the Sitnikov Problem near the 3/2 Commensurability |
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| Authors: | M A Jalali S H Pourtakdoust |
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| Institution: | (1) Mechanical Engineering Department, Applied Mechanics Division, Iran;(2) Mechanical Engineering Department, Aerospace Division, Sharif University of Technology, P.O. Box 11365, 9567,Azadi Ave., Tehran, Iran |
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| Abstract: | Regular solutions at the 3/2 commensurability are investigated forSitnikov s problem. Utilizing a rotating coordinate system and theaveraging method, approximate analytical equations are obtained for thePoincare sections by means of Jacobian elliptic functions and 3 periodicsolutions are generated explicitly. It is revealed that the system exhibitsheteroclinic orbits to saddle points. It is also shown that chaotic regionemerging from the destroyed invariant tori, can easily be seen for certaineccentricities. The procedure of the current study provides reliable answersfor the long-time behavior of the system near resonances. |
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| Keywords: | Sitnikov s problem" target="_blank">gif" alt="rsquo" align="BASELINE" BORDER="0">s problem periodic motion resonances chaotic behavior |
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