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In mathematics, a rotating body is commonly represented by a pseudovector along the axis of rotation. The length of the vector gives the speed of rotation and the direction of the axis gives the direction of rotation according to the right-hand rule: right fingers curled in the direction of rotation and the right thumb pointing in the positive ...
With symmetric tops, the selection rule for electric-dipole-allowed pure rotation transitions is ΔK = 0, ΔJ = ±1. Since these transitions are due to absorption (or emission) of a single photon with a spin of one, conservation of angular momentum implies that the molecular angular momentum can change by at most one unit. [11]
Listing's law, named after German mathematician Johann Benedict Listing (1808–1882), describes the three-dimensional orientation of the eye and its axes of rotation. Listing's law has been shown to hold when the head is stationary and upright and gaze is directed toward far targets, i.e., when the eyes are either fixating, making saccades, or pursuing moving visual targets.
A basic 3D rotation (also called elemental rotation) is a rotation about one of the axes of a coordinate system. The following three basic rotation matrices rotate vectors by an angle θ about the x -, y -, or z -axis, in three dimensions, using the right-hand rule —which codifies their alternating signs.
Rotational–vibrational spectroscopy is a branch of molecular spectroscopy that is concerned with infrared and Raman spectra of molecules in the gas phase.Transitions involving changes in both vibrational and rotational states can be abbreviated as rovibrational (or ro-vibrational) transitions.
The rotation matrices about the ... The general commutation rules are summarized by ... One of the consequences of Fermi–Dirac statistics is the exclusion ...
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For example, a reaction that is conrotatory can still rotate in two directions, producing enantiomeric products. A reaction that is torquoselective restricts one of these directions of rotation (partially or completely) to produce a product in enantiomeric excess. Disrotatory ring closing reaction