Journal of Theoretical
and Applied Mechanics

32, 2, pp. 377-394, Warsaw 1994

Formulation of constrained system dynamics by orthonormalizing the configuration space

Wojciech Blajer
An automatic computer code for constructing an orthonormal and differentiable basis of tangent (null) subspace for constrained mechanical systems is proposed. The methoa uses the Gram-Schmidt vector orthogonalization process, adopted according to the Riemannian space formalism. An interesting and useful peculiarity of the formulation is that the minimal-order (purely kinetic) equations of motion are generated directly in the resolved form (the related mass matrix is the identity matrix). The other problems solved are: generation of a well-posed and sparse supplementary matrix to the constraint matrix, used in the orthonorma-lization process; diminishing the constraint violation due to numerical errors of integration; estimation of consistent initial values of tangent velocities; and effective determination of constraint reactions.