Applying the point of view of non-holonomic mechanics, we arrive at a new and simple system of equations for the normal sub-Riemannian geodesics. These use a partial connection that is canonically available, given a choice of complement to the distribution. We also describe conditions which, if satisfied, mean that even this choice of complement is determined canonically, and that this determines a distinguished connection on the tangent bundle.

The geodesic equations obtained split into mutually driving horizontal and complementary parts. The method facilitates efficient choices of adapted coframes and reveals structures that are reminiscent of tractor calculi. We illustrate the features on examples, including some with non-constant symbols.

应用非完整力学的观点，我们得出了一个新的、简单的正规亚黎曼测地线方程组。这些使用规范可用的部分连接，给定分布的补充选择。我们还描述了条件，如果满足，则意味着即使是这种补集的选择也是规范确定的，并且这确定了切丛上的显着连接。

获得的测地线方程分为相互驱动的水平部分和互补部分。该方法有助于有效选择适应的共框并揭示让人​​联想到拖拉机结石的结构。我们在示例中说明了特征，包括一些带有非常量符号的特征。