This paper studies hamiltonization of nonholonomic systems using geometric tools, building on [1], [5]. The main novelty in this paper is the use of symmetries and suitable first integrals of the system to explicitly define a new bracket on the reduced space that codifies the nonholonomic dynamics and carries, additionally, an almost symplectic foliation (determined by the common level sets of the first integrals); in particular cases of interest, this new bracket is a Poisson structure that hamiltonizes the system. Our construction of the new bracket is based on a gauge transformation of the nonholonomic bracket by a global 2-form that we explicitly describe. We study various geometric features of the reduced brackets and apply our formulas to obtain a geometric proof of the hamiltonization of a homogeneous ball rolling without sliding in the interior side of a convex surface of revolution.

本文基于[1]，[5]，研究了使用几何工具对非完整系统的哈密顿化。本文的主要新颖之处是利用系统的对称性和合适的第一积分在缩减的空间上明确定义了一个新的括号，该括号将非完整动力学编成代码，并带有几乎辛的叶状结构（由共同的水平集确定）。第一积分）；在特定的情况下，这个新的支架是泊松结构，可以使系统汉普顿化。我们新托架的构建基于非完整托架通过我们明确描述的全局2形式的规范转换。