Is friction necessary for a Tractrix Curve? Is friction necessary for a 
Tractrix Curve? 


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*If friction is necessary, what curve will the particle trace if friction is not present?

*If friction is not necessary, what curve will the particle trace if friction is present?

*Does the setup have a string or a rigid rod attached to the tractor?
I have asked this on a Physics forum to understand the Physics more than the Maths behind this question.
NOTE This came when a question was asked on a WhatsApp group on physics I was part of. My level of physics is nowhere near to solve this problem, but the person who solved on the group did it by assuming friction was not present. But Wikipedia said friction is present. I was confused, hence this question.
 A: The tractrix is a curve defined by constraints and geometry, not physics and forces. It can only be realised physically under ideal conditions. Your colleague probably solved the mathematical (geometrical) problem, not the physical (dynamical) problem. The geometrical problem is far easier.   
As the wikipedia article says, to get a tractrix the object must move at an infinitessimally slow speed. The reason for this is that there must be no inertia involved. If an object with mass is being dragged at a finite speed then it tends to move in its current direction, rather than in the direction of the puller. Then the trajectory is more complicated than a tractrix. However, if friction is very high the mass will move in a series of jerks always directed towards the puller. 
The pulled object must remain a fixed distance from the puller. If a rope is used for pulling, it must remain taut. Using a massless rod is better, particularly if some pushing is required (see wikipedia animation 'pulling a pole'). 
If there is no friction the trajectory is determined solely by inertia. When the puller O is stationary the trajectory without friction is a point (no motion) whereas without friction it is a circle. When O accelerates along a straight line the general trajectory reative to O is a pendulum-like oscillation. Other motion can be surprisingly complex - eg when O oscillates along  a straight line. See Two objects connected by a rigid rod, one of which follows a determined path.

It is difficult to be more specific unless you provide the details of the problem which you are asking about.
