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I'm a novice to physics, so maybe it's rather stupid.

According to wiki, the tractrix could be considered a trajectory:

Suppose $AB$ is a stick on a smooth plane $\pi$, and the initial position of $AB$ is $A_0B_0$. $\mathbf v$ is a vector on $\pi$ such that $\mathbf v\perp \overrightarrow{A_0B_0}$ (It's not necessary, but it simplifies the problem). Now let's drag $B$ side of the stick $AB$ such that the speed is constantly $\mathbf v_B=\mathbf v$, then the locus of $A$ is a tractrix.

I tried to solve out the equation of that locus and then prove that it's a tractrix, but failed because I don't know the exact properties of a stick. Somebody told me that $\mathbf v_A\parallel\overrightarrow{AB}$ any time the stick is moving, but I can't prove that.

Can anybody help me formulate all the properties of sticks (just as properties of $\mathbb N$ in Peano's axiom system), well, there're something trivial, for example, $\left\lvert\overrightarrow{AB}\right\rvert$ is constant, and prove that $\mathbf v_A\parallel\overrightarrow{AB}$?


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Well, I'm not a novice to physics and I've never heard of a tractrix before, so I don't think it's a silly question! According to wiki they are assuming that the motion is heavily damped, so the only thing that makes sense to my intuition is that any motion of A orthogonal to AB is just damped to the point of insignificance. Motion parallel to AB is forced due to the constraint that the length be constant. It's a very idealized situation. To make it a real physics problem the rod needs to have mass and you need to know something about the friction/viscosity causing the damping. – Michael Brown Feb 18 '13 at 4:42
I feel the pole overcomplicates things. I learned of tractrices (indeed the only time I've heard them mentioned) in an old engineering book as the curve taken by a point mass dragged by a rope in a viscous medium (so that velocity is proportional to force at all times). Think of towing a boat on a rope while walking along a dock. Then you can see that the velocity must be parallel to the vector connecting A and B, since the rope will be taut. – Chris White Feb 18 '13 at 10:24

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