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

dx dt dy di =y+x-x(x + y) =-x+y-y(x + y) (12.7)

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A First Course In Mathematical Modeling

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Authors: Frank R. Giordano, William P. Fox, Steven B. Horton

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Question Posted: Jan 27, 2024 10:00 PM

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For the system (12.7), show that any trajectory starting on the unit circle x 2 + y

Question:

dx dt dy di =y+x-x(x + y) =-x+y-y(x + y) (12.7)

Step by Step Answer:

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

A First Course In Mathematical Modeling

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