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
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.