Formulation of Equations of Motion for Systems Subject to Constraints

A method for constructing equations of motion governing constrained systems is presented. The method, which is particularly useful when equations of motion have already been formulated, and new equations of motion, reflecting the presence of additional constraints are needed, allow the new equations to be written as a recombination of terms comprising the original equations. An explicit form in which the new dynamical equations may be cast for the purpose of numerical integration is developed, along with special cases that demonstrate how the procedure may be simplified in two commonly occurring situations. An illustrative example from the field of robotics is presented, and several areas of application are identified.