For the system (12.7), show that any trajectory starting on the unit circle x 2 + y
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For the system (12.7), show that any trajectory starting on the unit circle x2 + y2 = 1 will traverse the unit circle in a periodic solution. First introduce polar coordinates and rewrite the system as dr/dt = r(1–r2) and dθ/dt = 1.
Equation 12.7
Transcribed Image Text:
dx dt dy di =y+x-x(x + y) =-x+y-y(x + y) (12.7)
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To analyze the system given by equation 127 in terms of polar coordinates we need to convert the Cartesian coordinates x and y to polar coordinates r ...View the full answer
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Related Book For
A First Course In Mathematical Modeling
ISBN: 9781285050904
5th Edition
Authors: Frank R. Giordano, William P. Fox, Steven B. Horton
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