Gaussian, or isokinetic, dynamics was introduced by
Hoover and Evans in 1982. This is the idea:
be a (non-holonomic) constraint to the Newtonian motion of the
-particle system. This is only one constraint equation for
variables, thus we have some freedom of choice.
A dynamical constraint may always be put in terms of
constraint forces. A particularly economical and ``impartial'' prescription for the definition of these forces was given by
C. F. Gauss in 1829:
for all times we have
(with the Newtonian forces and the yet unknown constraint
forces ) we have
Among all possible sets of constraint forces let us choose the one with
the smallest norm. Requiring
we find, upon variation, that
for all physically allowed variations we have
we conclude that
. Inserting this in
The equations of motion according to Gauss and Hoover are thus
These e.o.m. lead to a deterministic trajectory with .
Note that and are needed at the same time step;
thus the usual Verlet algorithm is not applicable here. Instead, a
Predictor-Corrector algorithm or Runge-Kutta should be used.