A geometric approach to the solution of the dynamic response of constrained mechanical systems is proposed. A continuous and differentiable basis of the constraint null space is automatically generated using the Gram-Schmidt process. The independent coordinates are obtained by transforming the physical velocity coordinates to the tangent hyperplane of the constraint surface. As a result the independent coordinates lie on the constraint surface and no constraint violation control is necessary.
A Differentiable Null Space Method for Constrained Dynamic Analysis
Liang, C. G., and Lance, G. M. (September 1, 1987). "A Differentiable Null Space Method for Constrained Dynamic Analysis." ASME. J. Mech., Trans., and Automation. September 1987; 109(3): 405–411. https://doi.org/10.1115/1.3258810
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