EFFICIENT ALGORITHMS FOR SIMULATING COMPLEX MECHANICAL SYSTEMS USING CONSTRAINT DYNAMICS

The constrained Lagrangian and constrained Hamiltonian equations of mo tion for a general non-relativistic classical mechanical system subjec t to rheonomous holonomic constraints are derived in an easy and strai ghtforward manner. The numerical integration of the constrained equati ons of motion are discussed. It is shown how constraint errors introdu ced by the numerical integration can be avoided by introducing simple constraint correction schemes. As an example, the developed constraine d methods are applied to the periodically driven inverted n-linked pen dulum. It is demonstrated how the constrained methods leads to very ef ficient numerical algorithms. In the case of the n-linked pendulum, th e computational complexity using the constrained methods is O(n) compa red to O(n(3)) using the conventional unconstrained approach.