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SPIRAL OF THE HYPERBOLIC TANGENT


Polar equation: .

For k = 1/2:
Polar tangential angle: .

Curvilinear abscissa: .

Radius of curvature: .

Spiral with an asymptotic circle with the above equation (animation in the header for k ranging from 0 to 3).
 
 
This curve is the projection on xOy of the spherical curve: 

SPIRAL OF THE HYPERBOLIC COTANGENT


 
Polar equation: .

For k = 1/2:
Polar tangential angle.
 

Radius of curvature: .

Cf. the Poinsot spiral.
 
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© Robert FERRÉOL 2017