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GyroFilter
3D

GyroFilter[{Ixx, Iyy, Izz, Ixy, Iyz, Izx}, {x, y, z}] returns a new set of inertia properties that have zero inertia in the direction of {x, y, z}.
• The vector {x, y, z} must be a principal axis of the inertia properties, and the two principal moments not associated with {x, y, z} must be equal.

Inertia[GyroFilter[inertia, vector]] . vector always returns the zero vector, which shows that a body represented by the new inertia properties has no angular momentum if rotating about vector.
GyroFilter is normally used to filter out components of the inertia tensor that are modeled as zero-torque spinning motion with GyroMoment.
• It is never necessary to use GyroFilter if the gyro body is attached to the rest of the model by a zero-torque constraint, like a revolute or cylindrical joint.
• Use Inertia->GyroFilter[inertia, vector] as an option for Body to eliminate the axial torques related to angular acceleration of the body, and then use the unfiltered inertia properties with GyroMoment to model the gyroscopic torques.
• The inertia properties may also be given as a full inertia matrix.
• See also: ParallelAxis, PrincipalAxes.

Further Examples

Load the Modeler3D package.

Here GyroFilter is used to filter out the principal moment of inertia in the X direction.

We can rotate the inertia properties to another reference frame and still use GyroFilter to remove the principal moment.

We can show that the result is still effectively the same--the principal moment of inertia has been reduced to zero. Note that the last principal axis is equal to our rotated vector v.


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