next curve  previous curve  2D curves  3D curves  surfaces  fractals  polyhedra 
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.
next curve  previous curve  2D curves  3D curves  surfaces  fractals  polyhedra 
© Robert FERRÉOL 2017