If the change in
or
is deemed to be ``internal'', that is,
involving no external interactions, the appropriate accompanying
change in the internal state variables is that which conserves
energy. For the mass and its velocity, for example, we must have
where
since this holds the kinetic energy of the mass constant. Note that the momentum of the mass is changed, however, since
If the spring constant
is to change from
to
, the
instantaneous spring displacement
must satisfy
In a velocity-wave simulation, displacement is the integral of velocity. Therefore, the energy-conserving velocity correction is impulsive in this case.