Isokinetic Methods and Integration with Very Large Timestep

6 Isokinetic Methods and Integration with Very Lai e Timestep 

The starting point here is the Gaussian isokinetic thermostat [124], This type of constraint can be introduced into Newtonian dynamics q = M p, p = F q) by adding a Lagrange multiplier, i.e. changing the equations of motion to 

By differentiating the constraint and introducing the second equation, we obtain an equation for 

Simply substitute this expression into the differential equations to obtain the unconstrained equations 

These equations preservep M p constant. (Note. It is tempting to replace the denominator in this expression by Ko, the value of kinetic energy, but this is not recommended since it then destroys the first integral.) The system (8.37)-(8.38)can be rewritten in the aiternative form 

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