Corpus ID: 235417387

Symmetry in n-body problem via group representations

  title={Symmetry in n-body problem via group representations},
  author={Tingjie Zhou and Zhihong Xia},
We introduce an algebraic method to study local stability in the Newtonian n-body problem when certain symmetries are present. We use representation theory of groups to simplify the calculations of certain eigenvalue problems. The method should be applicable in many cases, we give two main examples here: the square central configurations with four equal masses, and the equilateral triangular configurations with three equal masses plus an additional mass of arbitrary size at the center. We… Expand

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