Search results
Results from the WOW.Com Content Network
In mathematics and physics, the plate trick, also known as Dirac's string trick (after Paul Dirac, who introduced and popularized it), [1] [2] the belt trick, or the Balinese cup trick (it appears in the Balinese candle dance), is any of several demonstrations of the idea that rotating an object with strings attached to it by 360 degrees does not return the system to its original state, while ...
A unit quaternion has the cosine of half the rotation angle as its scalar part and the sine of half the rotation angle multiplying a unit vector along some rotation axis (here assumed fixed) as its vector part (also called imaginary part, see Euler–Rodrigues formula). If the initial orientation of a rigid body (with unentangled connections to ...
corresponds to a vector rotation through an angle θ about an axis defined by a unit vector v = a 1 σ 1 + a 2 σ 2 + a 3 σ 3. As a special case, it is easy to see that, if v = σ 3, this reproduces the σ 1 σ 2 rotation considered in the previous section; and that such rotation leaves the coefficients of vectors in the σ 3 direction ...
The above definition is part of the ISQ, formalized in the international standard ISO 80000-3 (Space and time), [87] and adopted in the International System of Units (SI). [88] [89] Rotation count or number of revolutions is a quantity of dimension one, resulting from a ratio of angular displacement. It can be negative and also greater than 1 ...
In particular, if a beam of spin-oriented spin- 1 / 2 particles is split, and just one of the beams is rotated about the axis of its direction of motion and then recombined with the original beam, different interference effects are observed depending on the angle of rotation. In the case of rotation by 360°, cancellation effects are ...
In three dimensions, angular displacement is an entity with a direction and a magnitude. The direction specifies the axis of rotation, which always exists by virtue of the Euler's rotation theorem; the magnitude specifies the rotation in radians about that axis (using the right-hand rule to determine direction).
Rotation formalisms are focused on proper (orientation-preserving) motions of the Euclidean space with one fixed point, that a rotation refers to.Although physical motions with a fixed point are an important case (such as ones described in the center-of-mass frame, or motions of a joint), this approach creates a knowledge about all motions.
An interpretation that avoids this conflict is to say that the rotating spheres experiment does not really define rotation relative to anything in particular (for example, absolute space or fixed stars); rather the experiment is an operational definition of what is meant by the motion called absolute rotation. [2]