A generalized projection method for the dynamic analysis of constrained mechanical systems

The essence of the reported method lies in the partition of system configuration space into the orthogonal and tangent subspaces, denned relative to the constraint hypersurface. The projection of the initial (constraint reaction-contatntng) dynamical equations into the tangent subspace gives the constraint reaction-free (or canonical) equations of motion, whereas the orthogonal projection determines the associated constraint reactions. The proposed matrix/tensor/linear algebra mathematical formulation is suitable for the analysis carried out in generalized coordinates and/or quasi-velocities, and for systems subject to holonomic and/or nonholonomic constraints. Simplifications due to the use of independent coordinates/velocities are also discussed. An example illustrating these concepts is included.