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On a Periodic Solution of the 4-Body Problems

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  • Jian Chen
  • Bingyu Li

Abstract

We study the necessary and sufficient conditions on the masses for the periodic solution of planar 4-body problems, where three particles locate at the vertices of an equilateral triangle and rotate with constant angular velocity about a resting particle. We prove that the above periodic motion is a solution of Newtonian 4-body problems if and only if the resting particle is at the origin and the masses of the other three particles are equal and their angular velocity satisfies a special condition.

Suggested Citation

  • Jian Chen & Bingyu Li, 2014. "On a Periodic Solution of the 4-Body Problems," Advances in Mathematical Physics, Hindawi, vol. 2014, pages 1-3, February.
    • Handle: RePEc:hin:jnlamp:478495
    DOI: 10.1155/2014/478495
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