## Precession |

**Precession** is a change in the * nutation*. In

In astronomy, *precession* refers to any of several slow changes in an astronomical body's rotational or orbital parameters. An important example is the steady change in the orientation of the axis of rotation of the

Torque-free precession implies that no external moment (torque) is applied to the body. In torque-free precession, the *x*, *y*, *z*). If an object is asymmetric about its principal axis of rotation, the moment of inertia with respect to each coordinate direction will change with time, while preserving angular momentum. The result is that the

The torque-free precession rate of an object with an axis of symmetry, such as a disk, spinning about an axis not aligned with that axis of symmetry can be calculated as follows:^{[1]}

where **ω**_{p} is the precession rate, **ω**_{s} is the spin rate about the axis of symmetry, **I**_{s} is the moment of inertia about the axis of symmetry, **I**_{p} is moment of inertia about either of the other two equal perpendicular principal axes, and * α* is the angle between the moment of inertia direction and the symmetry axis.

When an object is not perfectly

For a generic solid object without any axis of symmetry, the evolution of the object's orientation, represented (for example) by a rotation matrix * R* that transforms internal to external coordinates, may be numerically simulated. Given the object's fixed internal

Precession occurs by repeatedly recalculating * ω* and applying a small

for the * ω*]

this unphysical tendency can be counteracted by repeatedly applying a small rotation vector * v* perpendicular to both