Rotation in three dimensions

Nutation

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. A pure nutation is a movement of a rotational axis such that the first Euler angle is constant. 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. (Wikipedia).

Nutation
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From playlist MIT RES.15-003 Shaping the Future of Work, Spring 2016

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From playlist Condense Logarithms with Brackets

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Condensing a logarithmic expression and simplifying the expression

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https://strings2015.icts.res.in/talkTitles.php

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Condensing a logarithmic expression with parenthesis

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From playlist Condense Logarithms with Brackets

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Condensing logarithmic expressions

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From playlist Condense Logarithms with Brackets

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Condensing logarithmic expressions

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From playlist Condense Logarithms with Brackets

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Related pages

Euler angles | Gyroscope | Circle of latitude | Top | Precession | Angular velocity | Rigid body dynamics | Axial precession | Cubic function | Azimuth | Earth's rotation | Lagrangian mechanics | Cross product | Cosine | Time derivative | Polar circle | Teetotum | Center of mass | Axial tilt | Leonhard Euler | Julian day