On a Periodic Solution of the 4-Body Problems

On a Periodic Solution of the 4-Body Problems

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We study the necessary and sufficient conditions on Network Cable Joiner 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 Dining Room Tables of the other three particles are equal and their angular velocity satisfies a special condition.