The three elemental rotations may be intrinsic ( rotations about the axes of the rotating coordinate system " XYZ ", solidary with the moving body, which changes its orientation after each elemental rotation ).
22.
If the motion is transformed to motion with respect to a rotating coordinate system ( with the rotating coordinate system co-rotating with the main circle ), then only the motion along the epi-circle remains.
23.
If the motion is transformed to motion with respect to a rotating coordinate system ( with the rotating coordinate system co-rotating with the main circle ), then only the motion along the epi-circle remains.
24.
This can be used to define a spinor as a column vector of 2 " s " + 1 components which transforms to a rotated coordinate system according to the spin matrix at a fixed point in space.
25.
:Image : Rotating _ fountain _ coriolis _ effect03 . gif is a sequence of 6 images, each depicting the centrifugal term and the coriolis term of the equation of motion for motion with respect to a rotating coordinate system.
26.
Here, "'? "'is the angular velocity of the rotating coordinate system with respect to the inertial coordinate system . " v " is velocity of the moving object with respect to the rotating coordinate system.
27.
Here, "'? "'is the angular velocity of the rotating coordinate system with respect to the inertial coordinate system . " v " is velocity of the moving object with respect to the rotating coordinate system.
28.
The concept of the centrifugal force can be applied in rotating devices, such as centrifuges, centrifugal pumps, centrifugal governors, and centrifugal clutches, and in centrifugal railways, planetary orbits, banked curves, etc . when they are analyzed in a rotating coordinate system.
29.
The abscissa, \ sigma _ \ mathrm { n }, and ordinate, \ tau _ \ mathrm { n }, of each point on the circle, are the magnitudes of the normal stress and shear stress components, respectively, acting on the rotated coordinate system.
30.
Since the vector of the coriolis term always points perpendicular to the velocity with respect to the rotating coordinate system, it follows that in the case of a restoring force that is a harmonic force, the eccentricity in the trajectory will show up as a small circular motion with respect to the rotating coordinate system.
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