论文标题
相对论力学和应用中的莫布图斯型原则
A Maupertuis-type principle in relativistic mechanics and applications
论文作者
论文摘要
我们为以下ode系统提供了一个莫布图斯型原理，特殊相对论：$$ \ frac {\ rm d} {{\ rm d} t} \ left（\ frac {m \ dot {x}} {\ sqrt {\ sqrt {1- | \ dot {x} |^2/c^2}} \ right）= \ nabla v（x） ω\ to \ mathbb {r} $是类$ c^1 $的函数。作为应用程序，我们证明存在具有相对论$ n $中心类型问题的多个周期性解决方案。
We provide a Maupertuis-type principle for the following system of ODE, of interest in special relativity: $$ \frac{\rm d}{{\rm d}t}\left(\frac{m\dot{x}}{\sqrt{1-|\dot{x}|^2/c^2}}\right)=\nabla V(x),\qquad x\inΩ\subset \mathbb{R}^n, $$ where $m, c > 0$ and $V: Ω\to \mathbb{R}$ is a function of class $C^1$. As an application, we prove the existence of multiple periodic solutions with prescribed energy for a relativistic $N$-centre type problem in the plane.
