多体系统中位移近似与模型修正

在建立多体系统动力学模型过程中，根据系统广义坐标的取值范围可以给出位移矢量的合理近似，但按照近似位移求得的速度和加速度却往往没有合理的精度，从而造成系统动力学模型的误差。利用约束的力学性质将系统位移所在的空间分解为互相正交的子空间，通过研究系统速度和加速度在这两个子空间的性质，提出了修正系统动力学模型的有效方法。

Approximation of displacement and model reforming in multi-body systems

The approximation of displacement, which is necessary in some cases, usually causes some errors in the model of multi body systems because of induced poor approximation of velocity and acceleration. By the properties of constraints in multi body systems, generalized displacement, velocity and acceleration vectors of multi body systems can be resolved in two subspaces, called tangent subspace and normal subspace, which are defined by the constraints and are orthogonal each other respectively. Component of the generalized velocity vector in tangent subspace is zeros and component of the generalized acceleration vector in normal subspaces can be valued without reference to equations of motion. Based on those observations this paper presents a theory to correct the model of multi body systems by modifying the velocity and acceleration and proves it by an example.