In this article we develop a theory of contact systems with nonholonomic constraints. We obtain the dynamics from Herglotz's variational principle, by restricting the variations so that they satisfy the nonholonomic constraints. We prove that the nonholonomic dynamics can be obtained as a projection of the unconstrained Hamiltonian vector field. Finally, we construct the nonholonomic bracket, which is an almost Jacobi bracket on the space of observables and provides the nonholonomic dynamics.

中文翻译：

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具有非完整约束的哈密顿系统和拉格朗日系统

在本文中，我们开发了具有非完整约束的接触系统理论。我们通过限制变化使它们满足非完整约束，从而从Herglotz的变分原理中获得动力学。我们证明非完整动力学可以作为无约束哈密顿向量场的投影而获得。最后，我们构造了非完整的括号，它是在可观测空间上几乎是雅可比的括号，并提供了非完整的动力学。