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Linear stability of homogeneous and quasi-homogeneous N-body problem by symmetry groups
- Publication Year :
- 2022
-
Abstract
- 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 $\alpha$-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.<br />Comment: 28 pages
- Subjects :
- Mathematics - Classical Analysis and ODEs
Subjects
Details
- Database :
- arXiv
- Publication Type :
- Report
- Accession number :
- edsarx.2207.06296
- Document Type :
- Working Paper