Ordinarily the motion of a string (whip) is described by the wave equation, where the tension is given by some physically-motivated formula. However, if we allow the string to move with the constraint that it is at all point inextensible, the tension is specified automatically through the solution of a boundary-value problem. Unfortunately, the tension is not always positive, so that the wave equation is not always of hyperbolic type. This makes a direct analysis of the PDE rather difficult.

However one can model an inextensible string by a collection of coupled rigid pendula (chain). In this case, one is dealing with a high-dimensional ordinary differential equation, which always has a solution. It turns out that this system approximates the partial differential equation surprisingly well, and one hopes that it's possible to construct a solution of the PDE by considering a Cauchy sequence of solutions of the ODEs. How this could happen will be the subject of my talk.

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