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Circular Motion Case

List of animations posted on this page.(Click the text to watch animation.)
Circular chase k = 1.25 case
Circular chase k = 1.075 case
Circular chase k = 1.10 case

This is the case when the Pursued will run on a Fixed circle with constant speed.
According to Ref.1,this problem seems not to have been solved until 1921 (F.V.Morley
and A.S.Hathaway)
Morley derived the differential equation and showed how to solve this equation by graphical methods. He also made a qualitative argument about how the curve should look like. What will be shown here are what he could have done if the computer and relevant software had been available in 1920's.

*************************** pursuit_circle_desc.dwg ***************************

Mathematical background


Example output

*************************** pursuit_circle_1_end.dwg ***************************

See the process in k = 1.25 case animation.

*************************** pursuit_circle_2_end.dwg ***************************

See the process in k = 1.075 case animation.

*************************** pursuit_circle_3_end.dwg ***************************

See the process in k = 1.10 case animation.

*************************** pursuit_circle.dwg ***************************

AutoCAD users:

Load an application program "pursuit.lsp": (load "pursuit")

: execute command : pursuit_circle


  1. Yates,Robert C. : A Handbook on Curves and their Properties. J.W.Edwards,Ann Arbor, p 170 & 206, 1947. This reference list the following as a reference
    American Mathematical Monthly,Vol. 28, 1921 p. 54, 91, 278

  2. Cohen, Abraham : An Elementary Treatise on Differential Equation. D.C.Heath and Co. p 173 & 326,1933.

  3. Simmons, George F. : Differential Equations with Applications and Historical Notes. McGraw-Hill, p. 52-58,1972.

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Last Updated Oct 9-th, 2006

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