Tractrix With Dog Leash Construction
The "Moving Plane" Attached To The Leash Draws Related Curves
Modify the curve
pen position on stick: -1.6 ... 3:
The tractrix family is defined by these equations:
c(t) = [stick*sin(t), stick*cos(t) + log(tang(t/2))].
The default is stick = 1 for the tractrix itsself.
These curves are obtained with tangents. For the simplest such
construction see:
Cycloid.
The caustic of the normals of the tractrix
is the Catenary.
The tractrix is usually explained by having a dog owner march on the
y-axis and pulling his resisting dog with a leash of length 1.
The leash (red) therefore is the tangent to the path of the dog. Knowing
the tangent, before knowing the curve, means:
the tractrix is determined by an ordinary differential equation (ODE) and
the given formula happens to be a solution.
Attach a "moving plane" to the leash - visualized by the square of random dots -
and let other points of this plane
draw related curves by changing the pen position on the leash/stick.