Planar and spatial joint constraint equations for jerk and jounce were derived for multibody dynamics. Exemplar derivations are provided. Results from kinematically driven numerical simulations of these new equations were compared to explicit geometric solutions for planar four-bar and inverted slider-crank mechanisms as well as spatial revolute-spherical-universal-revolute and revolute-spherical-prismatic-universal mechanisms. Root-mean-square-error between velocity, acceleration, jerk and jounce simulations versus explicit solutions were normalized by maximum absolute values for comparison. Relative precisions for new jerk and jounce computations were equivalent to relative precisions for extant velocity and acceleration computations. The new equations were significantly more accurate than finite difference approximations previously required for jerk and jounce. Third and fourth order kinematics developed for this paper are required to explore hyper-dynamic differential algebraic equations created by first and second derivatives of equations of motion for multibody systems using joint constraint methods.

中文翻译：

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具有关节约束的多体动力学的运动加加速度和颠簸

针对多体动力学推导了加加速度和颠簸的平面和空间关节约束方程。提供了示例推导。将这些新方程的运动学驱动数值模拟的结果与平面四杆和倒置曲柄滑块机构以及空间旋转-球面-万向-旋转和旋转-球面-棱柱-万向机构的显式几何解进行比较。速度、加速度、加加速度和颠簸模拟与显式解之间的均方根误差通过最大绝对值进行归一化以进行比较。新的加加速度和颠簸计算的相对精度相当于现有速度和加速度计算的相对精度。新方程比之前急动度和颠簸所需的有限差分近似更准确。本文开发的三阶和四阶运动学需要探索由使用关节约束方法的多体系统运动方程的一阶和二阶导数创建的超动态微分代数方程。