Pursuit Curve

Cartesian equation:
y = cx2 - log(x)

Click below to see one of the Associated curves.

Definitions of the Associated curves Evolute
Involute 1 Involute 2
Inverse curve wrt origin Inverse wrt another circle
Pedal curve wrt origin Pedal wrt another point
Negative pedal curve wrt origin Negative pedal wrt another point
Caustic wrt horizontal rays Caustic curve wrt another point

Click THIS LINK to experiment interactively with this curve and its associated curves.

If A moves along a known curve then P describes a pursuit curve if P is always directed towards A and A and P move with uniform velocities. These were considered in general by the French scientist Pierre Bouguer in 1732.

The case here is where A is on a straight line and was studied by Arthur Bernhart.

Pierre Bouguer was a French scientist who was the first to attempt to measure the density of the Earth using the deflection of a plumb line due to the attraction of a mountain. He made measurements in Peru in 1740. A more successful use of this method by the astronomer Maskelyne placed the density between 4.5 and 5.

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JOC/EFR/BS January 1997

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