In this study, we present explicit equations of motion for general mechanical systems exposed to holonomic and nonholonomic constraints based on the Gibbs-Appell formulation. Without constructing the Gibbs function, the proposed method provides a minimal set of first-order dynamic equations applicable for multibody constrained systems. Transforming the Newton–Euler equations from physical coordinates to quasivelocity spaces eliminate constraint reaction forces from motion equations. In this study, we develop a general procedure to select effective quasivelocities, which indicate that the proposed quasivelocities satisfy constraints, eliminate Lagrange multipliers, and reduce the number of dynamic equations to degrees of freedom. Besides, we test the validity and efficiency of the proposed approach using three constrained dynamical systems as illustrative examples. Finally, we compare the simulation results with Udwadia–Kalaba, augmented Lagrangian, and other conventional methods.

在这项研究中，我们基于 Gibbs-Appell 公式提出了暴露于完整和非完整约束的一般机械系统的明确运动方程。在不构造 Gibbs 函数的情况下，所提出的方法提供了适用于多体约束系统的最小一阶动力学方程组。将 Newton-Euler 方程从物理坐标转换到拟速度空间可以消除运动方程中的约束反作用力。在这项研究中，我们开发了一个选择有效准速度的一般程序，这表明所提出的准速度满足约束、消除拉格朗日乘子并将动态方程的数量减少到自由度。除了，我们使用三个受约束的动态系统作为说明性示例来测试所提出方法的有效性和效率。最后，我们将模拟结果与 Udwadia-Kalaba、增广拉格朗日和其他传统方法进行比较。