3体问题的变分极值性质

Variational Extremal Properties for 3-Body Problems

对Rk(k≥ 2 )中具有齐次势的 3体问题 ,我们证明了定义在 3个天体具有相同积分平均值的周期轨道空间上的Lagrange作用积分的极小值点正好是具有固定边长的等边三角形构型的圆周轨道。

For 3 body problems in R k(k≥2) with homogeneous potentials,we prove that the extremal points of the Lagrangian action integral defined on the periodic orbit space with the same integral mean for each body are exactly the planar equilateral triangle circular solutions and the side length of the equilateral triangle is fixed at any moment.