Coordinate Reduction in the Dynamics of Constrained Multibody Systems—A New Approach
Coordinate Reduction in the Dynamics of Constrained Multibody Systems—A New Approach
复制标题
约束多体系统动力学的坐标简化——一种新方法
DOI：
10.1115/1.3173739
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发表时间：
1988
期刊：
影响因子：
--
通讯作者：
F. Amirouche
中科院分区：
文献类型：
--
作者：
S. Ider;F. Amirouche
本文给出了m行n(n>；m)列线性无关的矩形矩阵的零空间的基的一个新的生成定理。该方法基于高斯行运算将约束雅可比矩阵变换为上三角矩阵。然后利用Gram-Schmidt过程来识别与上三角矩阵正交的基向量。然后，建立了构成满足代数约束方程的零空间的基的互补正交数组。给出了该定理在拉格朗日方程和凯恩方程的约束动力系统中的应用实例。给出了一种基于嵌入约束的凯恩方程的数值计算方法。该方法具有条件好、计算效率高、成本低等优点。
In this paper a new theorem for the generation of a basis for the null space of a rectangular matrix, with m linearly independent rows and n (n > m) columns is presented. The method is based on Gaussian row operations to transform the constraint Jacobian matrix to an uptriangular matrix. The Gram-Schmidt process is then utilized to identify basis vectors orthogonal to the uptriangular matrix. A complement orthogonal array which forms the basis for the null space for which the algebraic constraint equations are satisfied is then formulated. An illustration of the theorem application to constrained dynamical systems for both Lagrange and Kane’s equations is given. A numerical computer algorithm based on Kane’s equations with embedded constraints is also presented. The method proposed is well conditioned and computationally efficient and inexpensive.