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Nutate
Nutation is a rocking, swaying, or nodding motion in the axis of rotation of a largely axially symmetric object, such as a gyroscope or the Earth (see astronomical nutation). It may also refer to: * In biology: ** Nutation (botany), bending movements executed by some plant organs ** In human anatomy, movement of the sacrum vis-a-vis the ilia * The same as precession in spacecraft dynamics * Nutation (engineering) {{disambig ...
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Nutation
Nutation () 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. In a rigid body If a top is set at a tilt on a horizontal surface and spun rapidly, its rotational axis starts precessing about th ...
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Astronomical Nutation
Astronomical nutation is a phenomenon which causes the orientation of the axis of rotation of a spinning astronomical object to vary over time. It is caused by the gravitational forces of other nearby bodies acting upon the spinning object. Although they are caused by the same effect operating over different timescales, 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. An example of precession and nutation is the variation over time of the orientation of the axis of rotation of the Earth. This is important because the most commonly used frame of reference for measurement of the positions of astronomical objects is the Earth's equator — the so-called equatorial coordinate system. The effect of precession and nutation causes this frame of reference itself to change over time, relative to an arbitrary fixed frame. Nutation is o ...
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Nutation (botany)
Nutation refers to the bending movements of stems, roots, leaves and other plant organs caused by differences in growth in different parts of the organ. Circumnutation refers specifically to the circular movements often exhibited by the tips of growing plant stems, caused by repeating cycles of differences in growth around the sides of the elongating stem. Nutational movements are usually distinguished from 'variational' movements caused by temporary differences in the water pressure inside plant cells (turgor). Simple nutation occurs in flat leaves and flower petals, caused by unequal growth of the two sides of the surface. For example, in young leaf buds the outer surface of each leaflet grows faster, causing it to curve over its neighbors and form a compact bud. As the bud expands, growth becomes more rapid on the inner surface of the leaves, causing the bud to open and the leaves to flatten out. Similar inequality of growth, but more sharply localized, leads to the folding a ...
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Anatomical Terms Of Motion
Motion, the process of movement, is described using specific anatomical terms. Motion includes movement of organs, joints, limbs, and specific sections of the body. The terminology used describes this motion according to its direction relative to the anatomical position of the body parts involved. Anatomists and others use a unified set of terms to describe most of the movements, although other, more specialized terms are necessary for describing unique movements such as those of the hands, feet, and eyes. In general, motion is classified according to the anatomical plane it occurs in. ''Flexion'' and ''extension'' are examples of ''angular'' motions, in which two axes of a joint are brought closer together or moved further apart. ''Rotational'' motion may occur at other joints, for example the shoulder, and are described as ''internal'' or ''external''. Other terms, such as ''elevation'' and ''depression'', describe movement above or below the horizontal plane. Many anatomica ...
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Precession
Precession is a change in the orientation of the rotational axis of a rotating body. In an appropriate reference frame it can be defined as a change in the first Euler angle, whereas the third Euler angle defines the rotation itself. In other words, if the axis of rotation of a body is itself rotating about a second axis, that body is said to be precessing about the second axis. A motion in which the second Euler angle changes is called ''nutation''. In physics, there are two types of precession: torque-free and torque-induced. 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 Earth, known as the precession of the equinoxes. Torque-free Torque-free precession implies that no external moment (torque) is applied to the body. In torque-free precession, the angular momentum is a constant, but the angular velocit ...
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