具有齐次势的空间限制三体问题的非平面周期解

Periodic Solutions of the Restricted 3-Body Problem with Homogeneous Potentials

在本文中,我们用变分法研究一类具有齐次势的空间限制三体问题。我们先用变分极小化方法得到一个变分极小值点,然后应用雅克比必要条件证明该变分极小值点对应该空间限制三体问题的非平面周期解。

We use variational minimizing methods to study spatial restricted 3-body problems with a very small mass moving on the vertical axis of the moving plane for two masses. We assume the denominator ex- ponent in the potential energy depending on distances. We use Jacobi’s necessary condition to prove the periodic solution is nonconstant for any period.