论文标题
$ n $中的相对平衡延续 - 身体问题到恒定的空间
Continuation of relative equilibria in the $n$--body problem to spaces of constant curvature
论文作者
论文摘要
我们证明，对于这个参数的足够小值，可以继续使用恒定曲率$κ$（正或负的恒定曲率$κ$）的空间。我们还使用数值延续计算了某些经典相对平衡到弯曲空间的扩展。特别是，我们将带有不同质量的Lagrange的三角形配置扩展到正曲率和负曲率空间。
We prove that all non-degenerate relative equilibria of the planar Newtonian $n$--body problem can be continued to spaces of constant curvature $κ$, positive or negative, for small enough values of this parameter. We also compute the extension of some classical relative equilibria to curved spaces using numerical continuation. In particular, we extend Lagrange's triangle configuration with different masses to both positive and negative curvature spaces.
