What is "nutation"

Nutation \Nu*ta"tion\, n. [L. nutatio a nodding, fr. nutare to nod: cf. F. nutation.]

1. The act of nodding.

   So from the midmost the nutation spreads, Round and more round, o'er all the sea of heads.
   --Pope.

2. (Astron.) A very small libratory motion of the earth's axis, by which its inclination to the plane of the ecliptic is constantly varying by a small amount.

3. (Bot.)

   1. The motion of a flower in following the apparent movement of the sun, from the east in the morning to the west in the evening.

   2. Circumnutation.

1610s, "action of nodding," from Latin nutationem (nominative nutatio), noun of action from past participle stem of nutare "to nod," from PIE *neu- "to nod" (see numinous). Astronomical use is from 1715. Related: Nutational.

n. 1 (context physics English) a bobbing motion that accompanies the precession of a spinning rigid body 2 a nodding motion (of the head etc.) 3 (context astronomy English) any of several irregularities in the precession of the equinoxes caused by varying torque applied to the Earth by the Sun and the Moon 4 (context botany English) the circular motion of the tip of a growing shoot

n. uncontrolled nodding

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 behavior 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. In spacecraft dynamics, precession (a change in the first Euler angle) is sometimes referred to as nutation.

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. 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)

Nutation is the bending movements executed by some plant organs, such as stems, leaves, roots, etc., by which the part is inclined successively in various directions. Nutations are due to the unequal rate of growth of different sides of the organ, an inequality which, so far as is known at present (c. 1915), is dependent upon internal (unknown) causes and is not called forth by the action of external stimuli. The word is often used in a broad sense in the phrase nutational movement, to include all the movements in plants caused by growth in contrast to variation movements or movements produced by reversible turgor changes.

Simple nutation occurs in dorsiventral organs, such as flat leaves, both foliage and floral. The movements are only in one plane, depending upon the unequal growth of the opposite sides. When young the growth of the foliage leaves is most rapid upon their outer (dorsal) face, in consequence of which the leaf applies itself to the axis, arches over the apex, and with its neighbors forms a compact bud. Later growth becomes more rapid on the inner (ventral) face, the bud opens, and the leaves straighten out. Similar inequality of growth, but more sharply localized, leads to the folding and rolling of the leaf in the bud. Like movements of radial organs, such as stems, cylindrical leaves, and roots, have been termed circumnutation, or revolving nutation, to distinguish them from the simple nutation of dorsiventral organs. When any plant is in vigorous growth the axis rarely grows in length uniformly on all sides. The side on which growth is most rapid will push the apex over towards the side on which growth is less rapid. If the region of more rapid growth changes, shifting around the axis, the tip will be inclined successively to all points of the compass and with its simultaneous upward growth will describe a spiral, but, since the rate of growth is not uniform at successive intervals, the path described will be a very irregular spiral.

Movements quite similar to those above described are called forth in plant organs by external stimuli. Thus twining plants exhibit both true nutation and nutation due to geotropic sensitiveness. Changes in temperature cause flowers to open or close by movements which resemble the simple nutation of dorsiventral organs. Thus, the tulip, crocus, and other vernal flowers are very sensitive to changes in temperature. The crocus can perceive a change of 0.5°C (0.9°F), and will respond to a change of 20°C (36°F) in two minutes.

In engineering, a nutating motion is similar to that seen in a swashplate mechanism. In general, a nutating plate is carried on a skewed bearing on the main shaft and does not itself rotate, whereas a swashplate is fixed to the shaft and rotates with it. The motion is similar to the motions of coin or a tire wobbling on the ground after being dropped with the flat side down. Precession is the physical term that can refer to this kind of motion.

The nutating motion is widely employed in flowmeters and pumps. The displacement of volume for one revolution is first determined. The speed of the device in revolutions per unit time is measured. In the case of flowmeters, the product of the rotational speed and the displacement per revolution is then taken to find the flow rate.

A nutating disc engine was patented in 1993 and a prototype was reported in 2006. The engine consisted of an internal disk wobbling on a Z-shaped shaft. Nutation has also been used in drive systems for gearboxes, with proposed uses including helicopter rotors, seat recliners and a European Space Agency probe to Mercury.