论文标题
在非世俗系统中存在不变体积的存在
Existence of invariant volumes in nonholonomic systems subject to nonlinear constraints
论文作者
论文摘要
我们得出了受非线性限制（遵守Chetaev规则）的非独立系统的条件，以保留平滑的体积形式。当应用于仿射约束时，这些条件规定，只有当某个1形式确切而某个函数消失时，就存在基本的不变密度（此函数会自动消失对于线性约束）。此外，该结果可以扩展到用于任意度量连接的地球流量，并且足够的条件表现为扭转的整合性。结果，非独立系统的体积进行保护与非体力学连接的扭转密切相关。考虑了非线性/仿射/线性约束的示例。
We derive conditions for a nonholonomic system subject to nonlinear constraints (obeying Chetaev's rule) to preserve a smooth volume form. When applied to affine constraints, these conditions dictate that a basic invariant density exists if and only if a certain 1-form is exact and a certain function vanishes (this function automatically vanishes for linear constraints). Moreover, this result can be extended to geodesic flows for arbitrary metric connections and the sufficient condition manifests as integrability of the torsion. As a consequence, volume-preservation of a nonholonomic system is closely related to the torsion of the nonholonomic connection. Examples of nonlinear/affine/linear constraints are considered.
