We introduce the notion of a nonlinear splitting on a fibre bundle as a generalization of an Ehresmann connection. We present its basic properties and we pay attention to the special cases of affine, homogeneous and principal nonlinear splittings. We explain where nonlinear splittings appear in the context of Lagrangian systems and Finsler geometry and we show their relation to Routh symmetry reduction, submersive second-order differential equations and unreduction. We define a curvature map for a nonlinear splitting, and we indicate where this concept appears in the context of nonholonomic systems with affine constraints and Lagrangian systems of magnetic type.

我们引入了纤维丛上的非线性分裂的概念作为 Ehresmann 连接的推广。我们介绍了它的基本性质，并关注仿射、齐次和主非线性分裂的特殊情况。我们解释了非线性分裂在拉格朗日系统和芬斯勒几何的上下文中出现的位置，并展示了它们与劳斯对称约简、浸入式二阶微分方程和非约简的关系。我们为非线性分裂定义了一个曲率图，并指出了这个概念在具有仿射约束的非完整系统和磁性类型的拉格朗日系统的上下文中出现的位置。