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ROTATING ROD SPIRAL


Homemade name.

 
Polar equation: .

The rotating rod spiral is the trajectory of a massive ring sliding without friction on a horizontal rod in rotation around a centre. See on this website a derivation of the polar equation above, with k = 1.
 
Case b =  a: the equation can be written . Case b = - a: the equation can be written . Case b = -2a.

Note that the curve is similar to the curve in the first case if ab > 0 because, then, , and it is similar to the curve in the second case if ab < 0, because, then, ; in all the cases where a and b are not zero, the spiral therefore has a symmetry axis, like the Archimedean spiral; but the two infinite branches have asymptotes: the logarithmic spirals.
 
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© Robert FERRÉOL  2017