Nutation

This article is about the concept in physics. For the term in astronomy, see Astronomical nutation. For the term in mechanical engineering, see Nutation (engineering). For other uses, see Nutation (disambiguation).
Not to be confused with nunation or mutation.

Nutation (from Latin nūtātiō 'nodding, swaying') is a rocking, swaying, or nodding motion in the axis of rotation of a largely axially symmetric object, such as a gyroscope, planet, or bullet in flight, or as an intended behaviour of a mechanism.

In an appropriate reference frame it can be defined as a change in the second Euler angle. If it is not caused by forces external to the body, it is called free nutation or Euler nutation (after Leonhard Euler).

A pure nutation is a movement of a rotational axis such that the first Euler angle (or precession) is constant. Astronomers usually make a distinction between precession, which is a steady long-term change in the axis of rotation, and nutation, which is the combined effect of similar shorter-term variations. Therefore it can be seen that the circular red arrow in the planetary nutation diagram indicates the combined effects of precession and nutation, while nutation in the absence of precession would only change the tilt from vertical (second Euler angle). However, in spacecraft dynamics, precession (a change in the first Euler angle) is sometimes referred to as nutation.

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