论文标题
径向动力学非体力学轨迹是里曼尼亚的大地测量学！
Radial kinetic nonholonomic trajectories are Riemannian geodesics!
论文作者
论文摘要
非单学力学描述了受到不可集成约束的系统的运动。它最引人注目的特性之一是，非自然方程的推导本质上不是变化。 {但是，在}本文中，我们证明（定理1.1）对于动力学的非实体性{systems}，从固定点$ q $开始的解决方案对于在图像submanifold $ {\ Mathcal m}^nh}^nh} _q $ expent expect的固定点$ q $开始是真正的地理测量。这意味着一个令人惊讶的结果：具有起点$ q $的动力学非单向轨迹，对于足够小的时间，将长度最小化为$ {\ Mathcal M}^{nh} {nh} _q $！
Nonholonomic mechanics describes the motion of systems constrained by nonintegrable constraints. One of its most remarkable properties is that the derivation of the nonholonomic equations is not variational in nature. {However, in} this paper, we prove (Theorem 1.1) that for kinetic nonholonomic {systems}, the solutions starting from a fixed point $q$ are true geodesics for a family of Riemannian metrics on the image submanifold ${\mathcal M}^{nh}_q$ of the nonholonomic exponential map. This implies a surprising result: the kinetic nonholonomic trajectories with starting point $q$, for sufficiently small times, minimize length in ${\mathcal M}^{nh}_q$!
