论文标题
对称组的同质和准同质N体问题的线性稳定性
Linear stability of homogeneous and quasi-homogeneous N-body problem by symmetry groups
论文作者
论文摘要
由小子最近在N体问题上应用对称组的工作，我们将使用此方法研究相对的等边三角形和平方构型的相对平衡。 在将相应的二阶方程线性化后，具有适当的坐标转换后，我们通过将每个$ 2N \ times 2n $矩阵分解为一系列$ 2 \ times 2 $矩阵来研究相对平衡的线性稳定性。
Motivated by Xia-Zhou's recent work on applying symmetry groups to the N-body problem, we will study relative equilibria of the equilateral triangle and the square configurations under $α$-homogeneous and quasi-homogeneous potentials with this method. After linearizing the corresponding second order equations, with appropriate coordinate transformations, we study the linear stability of the relative equilibria by decomposing each $2n\times 2n$ matrix into a series of $2\times 2$ matrices.
