Numerical Experiment with SHAKE

A concern might be that the change of the model from unconstrained to constrained could alter the properties of the system in a way that would affect the overal simulation results. In practice, it is normally found that the other model and sampling errors present mean that the errors due to using constraints are relatively minor, particularly if the constraints are limited to bond lengths only, and even less of a factor if the constraints are limited to the bonds between hydrogen atoms and heavier atoms in biomolecules. 

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These various techniques were recently applied to molecular simulations [11, 20]. Both of these articles used the rotation matrix formulation, together with either the explicit reduction-based integrator or the SHAKE method to preserve orthogonality directly. In numerical experiments with realistic model problems, both of these symplectic schemes were shown to exhibit vastly superior long term stability and accuracy (measured in terms of energy error) compared to quaternionic schemes. 

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