Rigid-body dynamics solves Newton's equations of
motion for rigid
collections of atoms (Goldstein 1980).
Atoms
are collected into rigid groups, the motion of which is determined by
summing the forces acting on all of a group's elements and integrating
the rigid-body equations of motion.
The atomic masses 
are defined through the topology statement
(Section 3.1.1). The initial atomic coordinates are
taken from the main coordinate set ( atom properties X,Y,Z).
After completion of a rigid-body dynamics run, the main coordinate
set contains the coordinates of the last step.
The initial velocities are taken from the atom properties VX,VY,VZ.
They must be initialized outside the rigid-body dynamics statement. After
completion of a rigid-body dynamics run, the velocities of the
last step are stored in the atom properties VX, VY, VZ.
After completion of the molecular dynamics calculation, the partial energy terms for the last molecular dynamics step are stored in the appropriate symbols. The name of the symbols is given by $<energy-term> (see Section 4.5). The overall energy (Eq. 4.1) is stored in the symbol $ENER; the rms gradient is stored in $GRAD. The value of the second energy function (Eq. 4.26) is returned in the symbol $PERT. In addition, the following symbols are declared: $TEMP, $TOTE, and $TOTK, which are respectively the temperature, total energy, and kinetic energy.
X-PLOR's implementation of rigid-body molecular dynamics follows the algorithm described by Head-Gordon and Brooks (1991). The algorithm treats each group as a continuous mass distribution located at the center-of-mass position defined by
and characterized by its inertia tensor 
,
which has as elements
Here the index J labels the rigid bodies, and the summation index i runs over all atoms comprising a particular group.