Dynamic approach of spiral density waves

in time and azimuthal angle. resulting motion in a frame which rotates at the angular velocity OmegaP=omega/m, in which the perturbational field is time-independent. The steady-state response in this frame is a mean rotation of the obejct at the relative angular velocity difference: omega-OmegaP, which carries the object around a distorted circle which contains postive integral m bumps. For m=2, the distorted circle looks like a closed oval in the OmegaP frame. consider next applying a pertubational gravitational field of the same time and angular structure to starts or gas clouds at different radii r. If the angular phase of the perturbational field is the same at all radii, the long axes of the ovals would then acquire an oval distortion(.

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