Nina del Ser - Mathematics
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figure 9: Ω 4 figure 10: Ω 9
figure 11: Ω 1 figure 12: Ω 22
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Secondary rotor spins clockwise
Here are curves with corresponding values of Ω, only this time they are negative. An exception was made for
figure 15 because Ω=-1 would have simply repeated one of the simple cases discussed above.
figure 13: Ω 4 figure 14: Ω 9
figure 15: Ω 3 figure 16: Ω 22
Closer inspection shows that the curves all seem to be following a trend: the number of axes of symmetry in
any given curve is defined by the angular speed of the secondary rotor (e.g the curve generated when Ω 9
shows rotational symmetry of order 9). What follows is a simple mathematical explanation for this behaviour.
Square and add together the x and y components in equation (5) to obtain an expression for r 2 :
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