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MASCOT CURVE

The name "Mascot curve" comes from the fact that the circle
can represent the edges of a regiment, and the point *M* a dog, mascot
of the regiment, turning around the regiment at constant speed.

This problem is a variation on a problem posed by Martin Gardner in 1960 (under the name "marching cadets and a trotting dog") in the Scientific American journal in the case of a square regiment.

We can also consider that it is the curve described by
a ship turning around another ship while maintaining a constant distance
between them.

If
and V are the respective speeds of the regiment and the mascot,
R the radius of the circle, and
the angle locating the mascot on the circle, then the kinetic equations
of motion are given by:
Distance travelled by the mascot when it completes one turn of the regiment: ( elliptic function of the second kind) i.e. when the mascot goes twice as fast as the regiment ( k = 2). |

The mascot curve looks like a trochoid
with a loop, but isn't one: the trochoid would correspond to the case where
the speed of the mascot is constant with respect to the *regiment*
instead of the *floor*.

In the example below where the mascot goes 1.5 times as fast as the regiment, notice the widening of the curve between the two loops:

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© Robert FERRÉOL 2017