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Encyclopedia > Precession
Precession of a gyroscope

Precession refers to a change in the direction of the axis of a rotating object. In physics, there are two types of precession, torque-free and torque-induced, the latter being discussed here in more detail. In certain contexts, "precession" may refer to the precession that the Earth experiences, the effects of this type of precession on astronomical observation, or to the precession of orbital objects. Precession refers to a change in the direction of the axis of a rotating object. ... Image File history File links Gyroscope_precession. ... Image File history File links Gyroscope_precession. ... Torque applied via an adjustable end wrench Relationship between force, torque, and momentum vectors in a rotating system In physics, torque (or often called a moment) can informally be thought of as rotational force or angular force which causes a change in rotational motion. ...

## Contents

Torque-free precession occurs when the axis of rotation differs slightly from an axis about which the object can rotate stably. Poinsot's construction is an elegant geometrical method for visualizing the torque-free motion of a rotating rigid body. For example, when a plate is thrown, the plate may have some rotation around an axis that is not its axis of symmetry. When the object is not perfectly solid, internal vortices will tend to damp torque-free precession. Poinsots construction is a geometrical method for visualizing the torque-free motion of a rotating rigid body. ... This is an article on the real vortex phenomena. ...

## Torque-induced

Torque-induced precession (gyroscopic precession) is the phenomenon in which the axis of a spinning object (e.g. a part of a gyroscope) "wobbles" when a torque is applied to it. The phenomenon is commonly seen in a spinning toy top, but all rotating objects can undergo precession. If the speed of the rotation and the magnitude of the torque are constant the axis will describe a cone, its movement at any instant being at right angles to the direction of the torque. In the case of a toy top, if the axis is not perfectly vertical the torque is applied by the force of gravity tending to tip it over. The axis of rotation of a rotating body is a line such that the distance between any point on the line and any point of the body remains constant under the rotation. ... A gyroscope For other uses, see Gyroscope (disambiguation). ... Torque applied via an adjustable end wrench Relationship between force, torque, and momentum vectors in a rotating system In physics, torque (or often called a moment) can informally be thought of as rotational force or angular force which causes a change in rotational motion. ... This article is about the toy. ... In physics, a net force acting on a body causes that body to accelerate; that is, to change its velocity. ... Gravity is a force of attraction that acts between bodies that have mass. ...

The response of a rotating system to an applied torque. When the device swivels, and some roll is added, the wheel tends to pitch.

The device depicted on the right here is gimbal mounted. From inside to outside there are three axes of rotation: the hub of the wheel, the gimbal axis and the vertical pivot. Image File history File links No higher resolution available. ... A gimbal is a mechanical device that allows the rotation of an object in multiple dimensions. ...

To distinguish between the two horizontal axes, rotation around the wheel hub will be called 'rolling', and rotation around the gimbal axis will be called 'pitching.' Rotation around the pivot axis is called 'spinning'.

First, imagine that the device is spinning around the pivot axis. Then some rotation around the wheelhub is added. Imagine the gimbal axis to be locked, so that the wheel cannot pitch. The gimbal axis has sensors, that measure whether there is a torque around the gimbal axis. Torque applied via an adjustable end wrench Relationship between force, torque, and momentum vectors in a rotating system In physics, torque (or often called a moment) can informally be thought of as rotational force or angular force which causes a change in rotational motion. ...

In the picture, a section of the wheel has been named 'dm1'. When the rolling starts, section dm1 is at the perimeter of the spinning motion. Section dm1 has a lot of velocity and as it is forced closer to the center of rotation, it tends to move in the direction of the top-left arrow in the diagram (shown at 45o in the direction of rolling). Section dm2 of the wheel starts out at the center of rotation, and thus initially has zero velocity before the wheel is rolled. A force would be required to increase section dm2's velocity to the velocity at the perimeter of the pivot axis' plane. If that force is not provided then section dm2's inertia will make it move in the direction of the top-right arrow. Note that both arrows point in the same direction.

The same reasoning applies for the bottom half of the wheel, but there the arrows point in the opposite direction to that of the top arrows. Combined over the entire wheel, there is a torque around the gimbal axis when some rolling is added to rotation around a vertical axis.

It is important to note that the torque around the gimbal axis arises without any delay; the response is instantaneous.

In the discussion above, the setup was kept unchanging by preventing rotation around the gimbal axis. In the case of a spinning top, when the spinning top is tilting, gravity exerts a torque. Instead of rolling over, the spinning top pitches. The pitching motion reorients the spinning top with respect to the torque that is being exerted. The result is that the torque exerted by gravity elicits gyroscopic precession rather than causing the spinning top to fall to its side.

Precession or gyroscopic considerations have an effect on bicycle performance at high speed. Precession is also the mechanism behind gyrocompasses. For other uses, see Bicycle (disambiguation). ... Cutaway of AnschÃ¼tz gyrocompass The following description refers to the gyrocompasses used on ships. ...

Gyroscopic precession also plays a large role in the flight controls on helicopters. Since the driving force behind helicopters is the rotor disk (which rotates), gyroscopic precession comes into play. If the rotor disk is to be tilted forward (to gain forward velocity), its rotation requires that the downward net force on the blade be applied roughly 90 degrees (depending on blade configuration) before, or when the blade is to one side of the pilot and rotating forward.

To ensure the pilot's inputs are correct, the aircraft has corrective linkages which vary the blade pitch in advance of the blade's position relative to the swashplate. Although the swashplate moves in the intuitively correct direction, the blade pitch links are arranged to transmit the pitch in advance of the blade's position. The swashplate is the device that translates the pilots (or autopilots) commands via the helicopter flight controls into motion of the main rotor blades. ...

## Physics

### Classical (Newtonian)

The torque caused by the two opposing forces Fg and -Fg causes a change in the angular momentum L in the direction of that torque. This causes the top to precess.

Precession is the result of the angular velocity of rotation and the angular velocity produced by the torque. It is an angular velocity about a line which makes an angle with the permanent rotation axis, and this angle lies in a plane at right angles to the plane of the couple producing the torque. The permanent axis must turn towards this line, since the body cannot continue to rotate about any line which is not a principal axis of maximum moment of inertia; that is, the permanent axis turns in a direction at right angles to that in which the torque might be expected to turn it. If the rotating body is symmetrical and its motion unconstrained, and if the torque on the spin axis is at right angles to that axis, the axis of precession will be perpendicular to both the spin axis and torque axis. Image File history File links No higher resolution available. ... Image File history File links No higher resolution available. ... Torque applied via an adjustable end wrench Relationship between force, torque, and momentum vectors in a rotating system In physics, torque (or often called a moment) can informally be thought of as rotational force or angular force which causes a change in rotational motion. ... Angular velocity describes the speed of rotation and the orientation of the instantaneous axis about which the rotation occurs. ...

Under these circumstances the angular velocity of precession is given by:

In which Is is the moment of inertia, is the angular velocity of spin about the spin axis, and Q is the torque. Using = , we find that the period of precession is given by: Moment of inertia, also called mass moment of inertia and, sometimes, the angular mass, (SI units kg mÂ², Former British units slug ft2), is the rotational analog of mass. ...

In which Is is the moment of inertia, Ts is the period of spin about the spin axis, and Q is the torque. In general the problem is more complicated than this, however. Moment of inertia, also called mass moment of inertia and, sometimes, the angular mass, (SI units kg mÂ², Former British units slug ft2), is the rotational analog of mass. ... Torque applied via an adjustable end wrench Relationship between force, torque, and momentum vectors in a rotating system In physics, torque (or often called a moment) can informally be thought of as rotational force or angular force which causes a change in rotational motion. ...

An informal explanation of Precession: In a classic beginning physics demonstration, the instructor stands on a swiveling platform and holds a spinning bicycle wheel at arm's length. The wheel is vertical and the instructor is standing still. The instructor then tilts the wheel toward horizontal. This causes the instructor to start spinning slowly on the platform. Bringing the wheel back to vertical and tilting it the other way makes the instructor spin the other way. Why?

Imagine the wheel as a collection of small particles. Particles want to move in a straight line. In order for them to move in a circle there must be a force accelerating the particles toward the center of the circle (acceleration is a change in speed or direction or both — in this case just direction). This force is ultimately provided by bonds between the atoms in the wheel and spokes.

What happens when the instructor turns the spinning wheel from vertical to horizontal? Consider a particle somewhere on the wheel. If the wheel weren't being tilted, it would be accelerated around the circle as always. But since the wheel is tilting, it now has to follow a new path. A change in path is an acceleration, which in turn requires force (from the instructor's hands, transmitted through the spokes to the rim). Now consider the particle opposite the first particle on the wheel. It also has to change path, but in the opposite direction. Since the forces on opposite sides are in opposite directions, the result is torque. Each pair of opposite particles on the wheel contributes to the torque that causes the instructor to turn on the platform.

Tilting the wheel the other direction produces torque in the opposite direction, slowing the instructor's spin and eventually reversing it.

### Relativistic

The special and general theories of relativity give three types of corrections to the Newtonian precession, of a gyroscope near a large mass such as the earth, described above. They are: Two-dimensional analogy of space-time curvature described in General Relativity. ...

• Thomas precession a special relativistic correction accounting for the observer being in a rotating non-inertial frame.
• de Sitter precession a general relativistic correction accounting for the schwarzschild metric of curved space near a large non-rotating mass.
• Lense-Thirring precession a general relativistic correction accounting for the frame dragging by the Kerr metric of curved space near a large rotating mass.

Thomas precession, named after L.H. Thomas, is a correction to the spin-orbit interaction in Quantum Mechanics, which takes into account the relativistic time dilation between the electron and the nucleus in hydrogenic atoms. ... This article does not cite any references or sources. ... This article does not cite any references or sources. ...

## Of the Earth's axis

Precessional movement.

The Earth goes through one complete precession cycle in a period of approximately 25,800 years, during which the positions of stars as measured in the equatorial coordinate system will slowly change; the change is actually due to the change of the coordinates. Over this cycle the Earth's north axial pole moves from where it is now, within 1° of Polaris, in a circle around the ecliptic pole, with an angular radius of about 23.5 degrees (or approximately 23 degrees 27 arcminutes [1]). The shift is 1 degree in 180 years, where the angle is taken from the observer, not from the center of the circle. The precession of Earths axis of rotation with respect to inertial space is also called the precession of the equinoxes. ... Precession of rotational axis relative to the direction to the Sun at perihelion and aphelion. ... Precession of rotational axis relative to the direction to the Sun at perihelion and aphelion. ... This article is about the astronomical object. ... The equatorial coordinate system is probably the most widely used celestial coordinate system, whose equatorial coordinates are: declination () right ascension () -also RA-, or hour angle () -also HA- It is the most closely related to the geographic coordinate system, because they use the same fundamental plane, and the same poles. ... For other uses, see Polaris (disambiguation). ...

Discovery of the precession of the equinoxes is generally attributed to the ancient Greek astronomer Hipparchus (ca. 150 B.C.), though the difference between the sidereal and tropical years was known to Aristarchus of Samos much earlier (ca. 280 B.C.). It was later explained by Newtonian physics. The Earth has a nonspherical shape, being oblate spheroid, bulging outward at the equator. The gravitational tidal forces of the Moon and Sun apply torque as they attempt to pull the equatorial bulge into the plane of the ecliptic. The portion of the precession due to the combined action of the Sun and the Moon is called lunisolar precession. For the Athenian tyrant, see Hipparchus (son of Pisistratus). ... The sidereal year is the time for the Sun to return to the same position in respect to the stars of the celestial sphere. ... A tropical year is the length of time that the Sun, as viewed from the Earth, takes to return to the same position along the ecliptic (its path among the stars on the celestial sphere). ... For other uses of this name, including the grammarian Aristarchus of Samothrace, see Aristarchus Statue of Aristarchus at Aristotle University in Thessalonica, Greece Aristarchus (Greek: á¼ˆÏÎ¯ÏƒÏ„Î±ÏÏ‡Î¿Ï‚; 310 BC - ca. ... Classical mechanics (commonly confused with Newtonian mechanics, which is a subfield thereof) is used for describing the motion of macroscopic objects, from projectiles to parts of machinery, as well as astronomical objects, such as spacecraft, planets, stars, and galaxies. ... An oblate spheroid is ellipsoid having a shorter axis and two equal longer axes. ... Comet Shoemaker-Levy 9 after breaking up under the influence of Jupiters tidal forces. ... This article is about Earths moon. ... Sol redirects here. ... An equatorial bulge is a planetological term which describes a bulge which a planet may have around its equator, distorting it into an oblate spheroid. ... The plane of the ecliptic is well seen in this picture from the 1994 lunar prospecting Clementine spacecraft. ...

## Of planetary orbits

Precession of the perihelion (very exaggerated)

The revolution of a planet in its orbit around the Sun is also a form of rotary motion. (In this case, the combined system of Earth and Sun is rotating.) So the axis of a planet's orbital plane will also precess over time. Stylized and exaggerated picture of the precession of the orbit of a planet around the sun. ... Stylized and exaggerated picture of the precession of the orbit of a planet around the sun. ... This article is about several astronomical terms (apogee & perigee, aphelion & perihelion, generic equivalents based on apsis, and related but rarer terms. ... Two bodies with a slight difference in mass orbiting around a common barycenter. ... Sol redirects here. ...

The major axis of each planet's elliptical orbit also precesses within its orbital plane, in response to perturbations in the form of the changing gravitational forces exerted by other planets. This is called perihelion precession or apsidal precession (see apsis). Discrepancies between the observed perihelion precession rate of the planet Mercury and that predicted by classical mechanics were prominent among the forms of experimental evidence leading to the acceptance of Einstein's Theory of Relativity, which predicted the anomalies accurately.[2] A diagram of Keplerian orbital elements. ... [[Link titleBold text // ]] This article is about the planet. ... Classical mechanics (commonly confused with Newtonian mechanics, which is a subfield thereof) is used for describing the motion of macroscopic objects, from projectiles to parts of machinery, as well as astronomical objects, such as spacecraft, planets, stars, and galaxies. ... â€œEinsteinâ€ redirects here. ... Two-dimensional analogy of space-time curvature described in General Relativity. ...

These periodic changes of Earth's orbital parameters, combined with the precession of the equinoxes and of the inclination of the Earth's axis on its orbit, are an important part of the astronomical theory of ice ages. For precession of the lunar orbit see lunar precession. For the science fiction novella by William Shunn, see Inclination (novella). ... Milankovitch cycles are the collective effect of changes in the Earths movements upon its climate, named after Serbian civil engineer and mathematician Milutin MilankoviÄ‡. The eccentricity, axial tilt, and precession of the Earths orbit vary in several patterns, resulting in 100,000 year ice age cycles of the... Variations in CO2, temperature and dust from the Vostok ice core over the last 400 000 years For the animated movie, see Ice Age (movie). ... The moons elliptical orbit precesses about once in just under 9 years. ...

A phenomenon analogous to apsidal precession is nodal precession (see orbital node), which affects the orientation of the orbital plane. An orbital node is one of the two points where an inclined orbit crosses a plane of reference (e. ...

Wikimedia Commons has media related to:
Precession

Image File history File links Commons-logo. ...

This article does not cite any references or sources. ... Larmor precession refers to the precession of the magnetic moments of electrons or atomic nucleii in atoms around the direction of an external magnetic field. ... This article does not cite any references or sources. ... Rotation (green), Precession (blue) and Nutation (red) of the Earth Nutation is a slight irregular motion (etymologically a nodding) in the axis of rotation of a largely axially symmetric object, such as a gyroscope or a planet. ... This article needs to be wikified. ... The precession of Earths axis of rotation with respect to inertial space is also called the precession of the equinoxes. ... For other uses, see Precession (disambiguation). ... Thomas precession, named after L.H. Thomas, is a correction to the spin-orbit interaction in Quantum Mechanics, which takes into account the relativistic time dilation between the electron and the nucleus in hydrogenic atoms. ...

## References

1. ^ Cook, David R. (1999). Tilt of Earth's Axis. Environmental Earth Science Archive, Ask A Scientist. United States Department of Energy. Retrieved on 2006-05-24.
2. ^ Max Born (1924), Einstein's Theory of Relativity (The 1962 Dover edition, page 348 lists a table documenting the observed and calculated values for the precession of the perihelion of Mercury, Venus, and Earth.)
• "Moon and Spica", StarDate July 14, 2005, University of Texas McDonald Observatory, [1]

Results from FactBites:

 Precession - definition of Precession in Encyclopedia (1188 words) The axis of the Earth undergoes precession due to a combination of the Earth's nonspherical shape (it is an oblate spheroid, bulging outward at the equator) and the gravitational tidal forces of the Moon and Sun applying torque as they attempt to pull the equatorial bulge into the plane of the ecliptic. Precession causes the cycle of seasons (tropical year) to be about 20.4 minutes less than the period for the earth to return to the same position with respect to the stars as one year previously (sidereal year). The precession of the orbit of the Earth is an important part of the astronomical theory of ice ages.
 Precession - Wikipedia, the free encyclopedia (1277 words) Precession is the resultant of the angular velocity of rotation and the angular velocity produced by the torque. The Earth's precession of the equinoxes is an important part of the astronomical theory of ice ages. Discrepancies between the observed perihelion precession rate of the planet Mercury and that predicted by classical mechanics were prominent among the forms of experimental evidence leading to the acceptance of Einstein's Theory of Relativity, which predicted the anomalies accurately.
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