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Routation

Subscribe to America's largest dictionary and get thousands more definitions and advanced search—ad free! And who put it there, anyway? Literally How to use a word that literally drives some people nuts.

Is Singular 'They' a Better Choice? Can you spell these 15 tricky spelling words? Can you spell these 10 commonly misspelled words?

The dictionary has been scrambled—can you put it back together? Login or Register. Save Word. Log In. Definition of rotation. Keep scrolling for more.

Synonyms for rotation Synonyms gyration , pirouette , reel , revolution , roll , spin , twirl , wheel , whirl Visit the Thesaurus for More.

Examples of rotation in a Sentence the rotation of the Earth around its axis the rotation of the Moon around the Earth The Earth makes one rotation every day.

Recent Examples on the Web Peralta and Burnes threw the ball well in spring training in Arizona and were competing for a spot in the starting rotation.

First Known Use of rotation circa , in the meaning defined at sense 1a 1. Learn More about rotation. Time Traveler for rotation The first known use of rotation was circa See more words from the same year.

Dictionary Entries near rotation rotating die head rotating internship rotating-wing aircraft rotation rotational fault rotational inertia rotational loss See More Nearby Entries.

More Definitions for rotation. Venus may be thought of as rotating slowly backward or being "upside down". The dwarf planet Pluto formerly considered a planet is anomalous in this and other ways.

The ratio of the two how heavy is it to start, stop, or otherwise change rotation is given by the moment of inertia.

The angular velocity vector an axial vector also describes the direction of the axis of rotation. Similarly the torque is an axial vector. The physics of the rotation around a fixed axis is mathematically described with the axis—angle representation of rotations.

According to the right-hand rule , the direction away from the observer is associated with clockwise rotation and the direction towards the observer with counterclockwise rotation, like a screw.

The laws of physics are currently believed to be invariant under any fixed rotation. Although they do appear to change when viewed from a rotating viewpoint: see rotating frame of reference.

In modern physical cosmology, the cosmological principle is the notion that the distribution of matter in the universe is homogeneous and isotropic when viewed on a large enough scale, since the forces are expected to act uniformly throughout the universe and have no preferred direction, and should, therefore, produce no observable irregularities in the large scale structuring over the course of evolution of the matter field that was initially laid down by the Big Bang.

In particular, for a system which behaves the same regardless of how it is oriented in space, its Lagrangian is rotationally invariant.

According to Noether's theorem , if the action the integral over time of its Lagrangian of a physical system is invariant under rotation, then angular momentum is conserved.

Euler rotations provide an alternative description of a rotation. It is a composition of three rotations defined as the movement obtained by changing one of the Euler angles while leaving the other two constant.

Euler rotations are never expressed in terms of the external frame, or in terms of the co-moving rotated body frame, but in a mixture.

They constitute a mixed axes of rotation system, where the first angle moves the line of nodes around the external axis z , the second rotates around the line of nodes and the third one is an intrinsic rotation around an axis fixed in the body that moves.

These rotations are called precession , nutation , and intrinsic rotation. In flight dynamics , the principal rotations described with Euler angles above are known as pitch , roll and yaw.

The term rotation is also used in aviation to refer to the upward pitch nose moves up of an aircraft, particularly when starting the climb after takeoff.

Principal rotations have the advantage of modelling a number of physical systems such as gimbals , and joysticks , so are easily visualised, and are a very compact way of storing a rotation.

But they are difficult to use in calculations as even simple operations like combining rotations are expensive to do, and suffer from a form of gimbal lock where the angles cannot be uniquely calculated for certain rotations.

Many amusement rides provide rotation. A Ferris wheel has a horizontal central axis, and parallel axes for each gondola, where the rotation is opposite, by gravity or mechanically.

As a result, at any time the orientation of the gondola is upright not rotated , just translated. The tip of the translation vector describes a circle.

A carousel provides rotation about a vertical axis. Many rides provide a combination of rotations about several axes. In Chair-O-Planes the rotation about the vertical axis is provided mechanically, while the rotation about the horizontal axis is due to the centripetal force.

In roller coaster inversions the rotation about the horizontal axis is one or more full cycles, where inertia keeps people in their seats. Rotation of a ball or other object, usually called spin , plays a role in many sports, including topspin and backspin in tennis , English , follow and draw in billiards and pool , curve balls in baseball , spin bowling in cricket , flying disc sports, etc.

Table tennis paddles are manufactured with different surface characteristics to allow the player to impart a greater or lesser amount of spin to the ball.

Rotation of a player one or more times around a vertical axis may be called spin in figure skating , twirling of the baton or the performer in baton twirling , or , , , etc.

Rotation of a player or performer one or more times around a horizontal axis may be called a flip , roll , somersault , heli , etc. Rotation of a player around a vertical axis, generally between and degrees, may be called a spin move and is used as a deceptive or avoidance maneuver, or in an attempt to play, pass, or receive a ball or puck, etc.

It is often seen in hockey , basketball , football of various codes, tennis , etc. The end result of any sequence of rotations of any object in 3D about a fixed point is always equivalent to a rotation about an axis.

However, an object may physically rotate in 3D about a fixed point on more than one axis simultaneously, in which case there is no single fixed axis of rotation - just the fixed point.

However, these two descriptions can be reconciled - such a physical motion can always be re-described in terms of a single axis of rotation, provided the orientation of that axis relative to the object is allowed to change moment by moment.

This is equivalent, for linear transformations, with saying that there is no direction in the place which is kept unchanged by a 2 dimensional rotation, except, of course, the identity.

The question of the existence of such a direction is the question of existence of an eigenvector for the matrix A representing the rotation.

A standard eigenvalue determination leads to the characteristic equation. The corresponding rotation axis must be defined to point in a direction that limits the rotation angle to not exceed degrees.

Because A has only real components, there is at least one real eigenvalue, and the remaining two eigenvalues must be complex conjugates of each other see Eigenvalues and eigenvectors Eigenvalues and the characteristic polynomial.

Knowing that 1 is an eigenvalue, it follows that the remaining two eigenvalues are complex conjugates of each other, but this does not imply that they are complex—they could be real with double multiplicity.

In the degenerate case of a zero rotation angle, the rotation matrix is the identity, and all three eigenvalues are 1 which is the only case for which the rotation axis is arbitrary.

A spectral analysis is not required to find the rotation axis. Consequently, the expense of an eigenvalue analysis can be avoided by simply normalizing this vector if it has a nonzero magnitude.

That is, any improper orthogonal 3x3 matrix may be decomposed as a proper rotation from which an axis of rotation can be found as described above followed by an inversion multiplication by As much as every tridimensional rotation has a rotation axis, also every tridimensional rotation has a plane, which is perpendicular to the rotation axis, and which is left invariant by the rotation.

The rotation, restricted to this plane, is an ordinary 2D rotation. The proof proceeds similarly to the above discussion.

First, suppose that all eigenvalues of the 3D rotation matrix A are real. This means that there is an orthogonal basis, made by the corresponding eigenvectors which are necessarily orthogonal , over which the effect of the rotation matrix is just stretching it.

Therefore, we don't have a proper rotation, but either the identity or the result of a sequence of reflections. It follows, then, that a proper rotation has some complex eigenvalue.

Let v be the corresponding eigenvector. Also, they are both real vectors by construction. Therefore, they span an invariant plane. This plane is orthogonal to the invariant axis, which corresponds to the remaining eigenvector of A, with eigenvalue 1, because of the orthogonality of the eigenvectors of A.

Routation Video

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Can you spell these 10 commonly misspelled words? The dictionary has been scrambled—can you put it back together? Login or Register. Save Word.

Log In. Definition of rotation. Keep scrolling for more. Synonyms for rotation Synonyms gyration , pirouette , reel , revolution , roll , spin , twirl , wheel , whirl Visit the Thesaurus for More.

Examples of rotation in a Sentence the rotation of the Earth around its axis the rotation of the Moon around the Earth The Earth makes one rotation every day.

Recent Examples on the Web Peralta and Burnes threw the ball well in spring training in Arizona and were competing for a spot in the starting rotation.

First Known Use of rotation circa , in the meaning defined at sense 1a 1. Learn More about rotation. Time Traveler for rotation The first known use of rotation was circa See more words from the same year.

Published by Houghton Mifflin Company. The motion of an object around an internal axis. A single complete cycle of such motion. See Note at revolution.

A transformation of a coordinate system in which the new axes have a specified angular displacement from their original position while the origin remains fixed.

All rights reserved. Boost Your Grammar! Try Now. On the fifth farm, this pattern was isolated in two houses in consecutive rotations during spring and summer One issue is the representation of the rigid body motions of rotations and translations as elements within the algebra.

The aim is to minimise this performance measure, and it has certain symmetries, namely rotations, reflections, and permutations of the hydrophone positions.

Existing approaches define penetration depth strictly in the translational sense and might not handle the object rotations properly.

Studies for soil quality assessment production is reduced and organic matter declined in all rotations. They used a wavelet approach that is scale-independent and therefore constrained their similarity measure to consider only object rotations.

In addition, a limited number of field studies have confirmed the ability of brassicas in rotations to suppress weeds, nematodes25 and fungal pathogens Furthermore, the order of the cases now becomes significant since the rules for single and double rotations assume that the red parent's sibling is black.

Such motions can always be represented as pure rotations, but around a mobile pole. The crop rotations compared intercropping and two sole crop rotations.

We will call the boundary components and fixed points of the rotations singularities. In that representation pure rotations correspond to the base being atomic.

Ver todos los ejemplos de rotation. Click on a collocation to see more examples of it. Estos ejemplos provienen del Cambridge English Corpus y de otras fuentes de Internet.

Ver todas las colocaciones con rotation. Traducciones de rotation en chino tradicional.

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