New Method for Constraints Violation Suppression

The problem of constraints violation associated with numerical integration of dynamical equations of motion subject to constraints is dealt with. A new method for the suppression of constraints violation is presented. The method involves the definition of old constraints and of new constraints, the removal of the old constraints and the imposition of the new constraints, and the evaluation, after each integration step, of changes in the integration variables resulting from the removal-imposition process. The method is shown to be superior to the classical Baumgarte's method for constraints violation suppression in three aspects. First, the constraint violation measure number, a quantity defined herein, is smaller. Second, the constraint violation measure number stabilizes after the first integration step and does not degrade with time. Finally, the new method makes the process of trial and error, required by Baumgarte's method for the determination of integration constants, unnecessary. The method is discussed in connection with holonomic and simple nonholonomic constraints. (Author)