Projection Continuation for Minimal Coordinate Set Dynamics of Constrained Systems
Projection Continuation for Minimal Coordinate Set Dynamics of Constrained Systems
复制标题
约束系统最小坐标集动力学的投影延拓
DOI：
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发表时间：
2021
期刊：
影响因子：
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通讯作者：
P. Masarati
中科院分区：
文献类型：
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作者：
Ping Zhou;A. Zanoni;P. Masarati
利用约束雅可比矩阵的QR分解来提取合适的子空间，并随着解的演化将QR分解与约束雅可比矩阵的演化结合起来，重新研究了约束系统动力学在局部与约束流形相切的子空间上的坐标投影公式。针对独立坐标的子空间，提出了一种真正的连续算法，该算法不会明显影响解的质量，但避免了由于坐标集的任意重参数化而导致的广义速度的人为算法不连续。通过求解简单的多自由度问题来证明这一性质，该问题有或没有所提出的延拓。
The formulation of constrained system dynamics using coordinate projection onto a subspace locally tangent to the constraint manifold is revisited using the QR factorization of the constraint Jacobian matrix to extract a suitable subspace, and integrating the evolution of the QR factorization along with that of the constraint Jacobian matrix, as the solution evolves. A true continuation algorithm is thus proposed for the subspace of independent coordinates, which does not visibly affect the quality of the solution, but avoids the artificial algorithmic discontinuities in the generalized velocities that would result from arbitrary reparameterization of the coordinate set. This property is exemplified by solving simple multi-degree-of-freedom problems with and without the proposed continuation.