A geometric environment for the study of non-holonomic Lagrangian systems is developed. A definition of admissible displacement valid in the presence of arbitrary non-linear kinetic constraints is proposed. The meaning of ideality for non-strictly mechanical systems is analyzed. The concepts of geometric and/or dynamical symmetry of a constrained system are discussed and embodied in a subsequent non-holonomic formulation of Noether theorem. A revisitation of the results in an “extrinsic” variational language is worked out. A few examples and an appendix illustrating some properties of the manifold of admissible kinetic states are presented.

中文翻译：

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非完整力学中的对称性和守恒定律

开发了用于研究非完整拉格朗日系统的几何环境。提出了在存在任意非线性动力学约束的情况下有效的容许位移定义。分析了非严格机械系统的理想性的含义。在随后的Noether定理的非完整公式中讨论并体现了受约束系统的几何和/或动力学对称性的概念。重新审视了“外在”变分语言中的结果。给出了几个例子和一个附录，说明了可允许的动力学状态流形的一些特性。