Chases and Escapes by Paul J. Nahin

Author:Paul J. Nahin [Nahin, Paul J.]
Language: eng
Format: epub
ISBN: 9781400842063
Published: 0101-01-01T00:00:00+00:00

3.2 The Symmetrical n-Bug Problem

The geometry of n bugs in a symmetric cyclic pursuit is shown in figure 3.2.1, for the situation of any two adjacent bugs, A and B. Without loss of generality I've chosen our coordinate axes such that bug A is initially on the horizontal axis (and so, of course, bug B is initially at angle 2π/n). The initial distance between bugs A and B (between any two adjacent bugs, in fact) is then 2r(0)sin(π/n), where the initial distance from the center C of the bugs' regular n-gon to each of the bugs is r (0), and r = r(t) denotes that distance for t ≥ 0. Each bug always moves directly toward its nearest counterclockwise neighbor with the same speed v (I am following the notation and approach of Watton and Kydon (1969)), that is, the speed of A is v directly along the line joining A to B, as shown in the figure. We can resolve this speed into two components, a radial component vr directed inward toward C, and a transverse component vθ directed perpendicular to vr. From figure 3.2.1, or from our results at the beginning of section 2.3, these speed components are

Download

Copyright Disclaimer:
This site does not store any files on its server. We only index and link to content provided by other sites. Please contact the content providers to delete copyright contents if any and email us, we'll remove relevant links or contents immediately.