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Mode Motions I

We provide an example of omega-mode motion here. We call this specific motion the cyclone, which consists of two parts:

1. The first part of the cyclone is an Archimedean spiral. This curve is defined by polar coordinates (r, θ), where r is a linear function of θ. In a cyclone motion, r decreases over time and, in the end, r = 0. Then the motion turns into the second part.
2. The second part of the cyclone motion is a spin, where v = 0 and ω > 0.

Watch the video, Cyclone. The transition from the spiral motion to the spinning motion is seamless. See the trajectory.

We can define any combination of v and w equations for an omega mode motion; hence, an infinite number of motions exist in this category.

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