Efficient Algorithms for Simulating Complex Mechanical Systems Using Constraint Dynamics

The constrained Lagrangian and constrained Hamiltonian equations of motion for a general non-relativistic classical mechanical system subject to rheonomous holonomic constraints are derived in an easy and straightforward manner.The numerical integration of the constrained equations of motion are discussed. It is shown how constraint errors introduced by the numerical integration can be avoided by introducing simple constraint correction schemes.As an example, the developed constrained methods are applied to the periodically driven inverted n-linked pendulum. It is demonstrated how the constrained methods leads to very efficient numerical algorithms. In the case of the n-linked pendulum, the computational complexity using the constrained methods is O(n) compared to O(n(3)) using the conventional unconstrained approach.