The six DOF solver in Ansys Fluent uses the object’s forces and moments in order to compute the translational and angular motion of the center of gravity of an object. The governing equation for the translational motion of the center of gravity is solved for in the inertial coordinate system:
 | (3–8) |
where 
is the translational motion of the center of gravity, 
is the mass, and 
is the force vector due to gravity.
The angular motion of the object, 
, is more easily computed using body coordinates:
 | (3–9) |
where 
is the inertia tensor, 
is the moment vector of the body, and 
is the rigid body angular velocity vector.
The moments are transformed from inertial to body coordinates using
 | (3–10) |
where, 
represents the following transformation matrix:
where, in generic terms, 
and 
. The angles 
, 
, and 
are Euler angles that represent
the following sequence of rotations:
rotation about the Z axis (for example, yaw for airplanes)
rotation about the Y axis (for example, pitch for airplanes)
rotation about the X axis (for example, roll for airplanes)
After the angular and the translational accelerations are computed from Equation 3–8 and Equation 3–9, the rates are derived by numerical integration [614]. The angular and translational velocities are used in the dynamic mesh calculations to update the rigid body position.