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Nutation
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{{Short description|Wobble of the axis of rotation}} {{about|the concept in physics|the term in astronomy|Astronomical nutation|the term in mechanical engineering|Nutation (engineering)|other uses}} {{distinguish|nunation}} [[File:Nutation.gif|thumb|Nutation of a sphere animation]] [[File:Praezession.svg|thumb|{{legend-line|green solid 2px|Rotation}} {{legend-line|blue solid 2px|Precession}}{{legend-line|red solid 2px|Nutation}}in obliquity of a planet]] '''Nutation''' ({{etymology|la|{{wikt-lang|la|nΕ«tΔtiΕ}}|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]] [[external ballistics|in flight]], or as an intended behaviour of a mechanism. In an appropriate [[frame of reference|reference frame]] it can be defined as a change in the second [[Euler angles#Euler rotations|Euler angle]]. If it is not caused by forces external to the body, it is called free nutation or Euler nutation (after [[Leonhard Euler]]).<ref name=Lowrie/> A pure nutation is a movement of a rotational axis such that the first Euler angle is constant.{{citation needed|date=August 2012}} Therefore it can be seen that the circular red arrow in the 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.<ref>{{cite book|last=Kasdin|first=N. Jeremy|title=Engineering dynamics : a comprehensive introduction|date=2010|publisher=[[Princeton University Press]]|location=Princeton, N.J.|isbn=9780691135373|pages=526β527|author2=Paley, Derek A. }}</ref>
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