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Page "Equivalence" ¶ 17
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Some Related Sentences

** and Improper
** Improper motivation

** and rotation
** Van-ness rotation / rotationplasty ( foot being turned around and reattached to allow the ankle joint to be used as a knee )
** blitting, rotation, stretching, reduction, alpha blending, Gouraud shading
** North Pole, the northernmost point on the surface of the Earth, where the Earth's axis of rotation intersects the Earth's surface
** South Pole, the southernmost point on the surface of the Earth, where the Earth's axis of rotation intersects the Earth's surface
** Stepper motor, a type of electric motor capable of rotating its output shaft in equally spaced fractions of a full rotation, known as steps
** Synthetic molecular motor, molecular machines capable of rotation under energy input
** Rotating variables, stars whose variability is caused by phenomena related to their rotation.
** Image scaling / rotation
** Modular rotation in sequences of thirds
** Charge exchange spectroscopy – provides impurity ion temperature, density and rotation profiles
** Diurnal motion, improper motion due to the Earth's rotation on its axis
** Wagon-wheel effect, temporal aliasing effect in which a spoked wheel appears to rotate differently from its true rotation
** Moment of inertia, a measure of an object's resistance to changes in its rotation rate
** Rotation around a fixed axis, a subset of rotation with more constraints
** Yaw ( rotation )
** an Aerobatic maneuver, rotation around the vertical axis
** Yaw rate sensor, angular speed of yaw rotation
** rotation about a point-3
** rotation about an axis-5
** rotation about an axis combined with translation along that axis ( screw operation )-6
** rotation about an axis by an angle not equal to 180 °, combined with reflection in a plane perpendicular to that axis ( roto-reflection )-6
** r is the distance from the axis of rotation,
** N-VCT — Varies the rotation of the cam ( s ) only, does not alter lift or duration of the valves.
** Terrell rotation, mathematical and physical effect

** and equivalence
** In the realm of relativistic many-bodied mechanics, namely the time-symmetric Wheeler – Feynman absorber theory: the equivalence between an advanced Liénard – Wiechert potential of particle j acting on particle i and the corresponding potential for particle i acting on particle j was demonstrated exhaustively to order before being proved mathematically.
** Graphing equivalence
** Turing equivalence ( theory of computation )
** Moral equivalence
** Logical equivalence
** Rotational equivalence
** Probabilistic equivalence
** Dynamic and formal equivalence
** Lorentz surface, a two-dimensional oriented smooth manifold with a conformal equivalence class of Lorentzian metrics.
** there is a one-to-one correspondence between outgoing edges of any two nodes of the same information set — thus the set of all outgoing edges of an information set is partitioned in equivalence classes, each class representing a possible choice for a player's move at some point —, and

Improper and rotation
Improper rotations correspond to orthogonal matrices with determinant − 1, and they do not form a group because the product of two improper rotations is a proper rotation.
# redirect Improper rotation
* Improper rotation producing an inversion
* Improper rotation
# redirect Improper rotation

rotation and equivalence
For a given geometric figure in a given geometric space, consider the following equivalence relation: two automorphisms of space are equivalent if and only if the two images of the figure are the same ( here " the same " does not mean something like e. g. " the same up to translation and rotation ", but it means " exactly the same ").
For doing this equivalence, we will have to define how will we represent a rotation with this 4D-embedded surface.
When the extrinsic rotations equivalence is used the given angles are inverted respect the former, meaning that the first angle is the intrinsic rotation and the last one the precession.
No geometrical information is lost when using the rotation equivalence because the static parameters can be calculated from the name of the convention.
Using the equivalence between Euler angles and rotation composition, it is possible to change to and from matrix convention.

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