AI 中文总结
本研究针对平面1+N共轨道牛顿体问题，证明带齐次势的1+5质量对称凸共轨道中心构型必具对称轴，并在角变量限制下证明其与凸1+N共轨道中心构型的线性稳定性。
AI 中文摘要
对于平面牛顿1+N体问题，当N个质量趋近于零时，对应的相对平衡态会围绕主导质量形成共轨道构型。本研究聚焦平面1+N共轨道问题中的凸中心构型，针对带齐次势的1+5共轨道问题，证明了任意质量对称的凸共轨道中心构型必存在一条对称轴；进一步，在齐次势角变量的明确限制下，证明了凸对称1+5及凸1+N共轨道中心构型的线性稳定性。
英文摘要
For the planar Newtonian 1+N-body problem when the N masses tend to zero, the corresponding relative equilibria become coorbital around the dominant mass. In this work, we focus on convex central configurations in the planar 1+N coorbital problem. For the 1+5 coorbital problem with the homogeneous potential, we prove that any convex coorbital central configuration with symmetric masses must have an axis of symmetry. Furthermore, under explicit restrictions on the angular variables in a homogeneous potential, we prove the linear stability of both convex symmetric 1+5 and convex 1+N coorbital central configurations.
Comments14 pages, 1 figures, 28 conferences
