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
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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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