Rotation  

In General > s.a. kinematics of special relativity; Reference Frame [rotating].
* In R3: An element R of SO(3), which can be parametrized by Euler angles, R(, , ) = R3() R1() R3().
* Vector fields: In generalized Cartesian coordinates,

1 = (0; 0, z, –y) ,       2 = (0; –z, 0, x) ,       3 = (0; y, –x, 0) ;

in spherical coordinates,

1 = (0; 0, sin, cot cos) ,       2 = (0; 0, –cos, cot sin) ,       3 = (0; 0, 0, –1) .

* Of a world-line: Its meaning is well-defined, not just wrt something – it can be measured by a spiked sphere with springs and beads; To define it quantitatively, introduce 3 orthogonal vectors ua, va and wa on the world-line; The rate of change of these vectors measures the rotation; There is no rotation iff m m ua = a (umAm), m m va = a (vmAm), and m m wa = a (wmAm), where a is the unit tangent to the world-line.
* Measurement: The most sensitive instruments are laser gyroscopes, and atom interferometers; The latter have sensitivities of one-hundredth of a degree/min [@ Lenef et al PRL(97) + pn(97)feb], and potentially much less.

Rotational Invariance in Physics > see hamiltonian dynamics; realism; spherical symmetry; [symmetry].

References > s.a. time [rotating clocks].
@ General references: Walker 90.
@ In general relativity: Malament gq/00-in [vs intuition]; Bel gq/03 [Wilson-Wilson, Michelson-Morley experiments]; Kajari et al a0905-in.
@ Rotation of the universe: Hawking Obs(69); Chaliasos ap/06 [rotation of galaxies and acceleration].
@ Teaching: Silva & Tavares AJP(07)jan [angular momentum and angular velocity].
@ Related concepts and systems: Lansey a0906/AJP [rotations through imaginary angles]; > s.a. angular momentum; stars.


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