Nonlinear Dynamics and Chaos
2nd Edition
ISBN: 9780813349107
Author: Steven H. Strogatz
Publisher: PERSEUS D
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Question
Chapter 7.1, Problem 1E
Interpretation Introduction
Interpretation:
To sketch the portrait for the system equation
Concept Introduction:
Fixed points are the points where
If
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Convert the equation, x? + y? = 4, from rectangular coordinates into polar coordinates. Solve for
%3D
r.
r(8) =
Enter theta for 0 if needed.
convert to an equation in polar coordinates of the form r = f (θ). y = x2
Rewrite the Cartesian equation x
5 as a polar equation.
r(0) =
Enter theta for 0 if needed.
Chapter 7 Solutions
Nonlinear Dynamics and Chaos
Ch. 7.1 - Prob. 1ECh. 7.1 - Prob. 2ECh. 7.1 - Prob. 3ECh. 7.1 - Prob. 4ECh. 7.1 - Prob. 5ECh. 7.1 - Prob. 6ECh. 7.1 - Prob. 7ECh. 7.1 - Prob. 8ECh. 7.1 - Prob. 9ECh. 7.2 - Prob. 1E
Ch. 7.2 - Prob. 2ECh. 7.2 - Prob. 3ECh. 7.2 - Prob. 4ECh. 7.2 - Prob. 5ECh. 7.2 - Prob. 6ECh. 7.2 - Prob. 7ECh. 7.2 - Prob. 8ECh. 7.2 - Prob. 9ECh. 7.2 - Prob. 10ECh. 7.2 - Prob. 11ECh. 7.2 - Prob. 12ECh. 7.2 - Prob. 13ECh. 7.2 - Prob. 14ECh. 7.2 - Prob. 15ECh. 7.2 - Prob. 16ECh. 7.2 - Prob. 17ECh. 7.2 - Prob. 18ECh. 7.2 - Prob. 19ECh. 7.3 - Prob. 1ECh. 7.3 - Prob. 2ECh. 7.3 - Prob. 3ECh. 7.3 - Prob. 4ECh. 7.3 - Prob. 5ECh. 7.3 - Prob. 6ECh. 7.3 - Prob. 7ECh. 7.3 - Prob. 8ECh. 7.3 - Prob. 9ECh. 7.3 - Prob. 10ECh. 7.3 - Prob. 11ECh. 7.3 - Prob. 12ECh. 7.4 - Prob. 1ECh. 7.4 - Prob. 2ECh. 7.5 - Prob. 1ECh. 7.5 - Prob. 2ECh. 7.5 - Prob. 3ECh. 7.5 - Prob. 4ECh. 7.5 - Prob. 5ECh. 7.5 - Prob. 6ECh. 7.5 - Prob. 7ECh. 7.6 - Prob. 1ECh. 7.6 - Prob. 2ECh. 7.6 - Prob. 3ECh. 7.6 - Prob. 4ECh. 7.6 - Prob. 5ECh. 7.6 - Prob. 6ECh. 7.6 - Prob. 7ECh. 7.6 - Prob. 8ECh. 7.6 - Prob. 9ECh. 7.6 - Prob. 10ECh. 7.6 - Prob. 11ECh. 7.6 - Prob. 12ECh. 7.6 - Prob. 13ECh. 7.6 - Prob. 14ECh. 7.6 - Prob. 15ECh. 7.6 - Prob. 16ECh. 7.6 - Prob. 17ECh. 7.6 - Prob. 18ECh. 7.6 - Prob. 19ECh. 7.6 - Prob. 20ECh. 7.6 - Prob. 21ECh. 7.6 - Prob. 22ECh. 7.6 - Prob. 23ECh. 7.6 - Prob. 24ECh. 7.6 - Prob. 25ECh. 7.6 - Prob. 26E
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- Write each equation in polar coordinates. Express as a function of t. Assume that r > 0. (a) y = 9 r = (b) z² + y? = 6 %3D (c) z? + y? + 10z = 0 r= (d) z (x² + y?) = 5y? r= Note: You can earn partial credit on this problem.arrow_forwardGraph the equations r = 2 and θ = π / 3 on the same set of polar axes.arrow_forwardRewrite the Cartesian equation x +y = 5 as a polar equation. Tip r(8) = %3D Enter theta for 0 if needed.arrow_forward
- Part III: Equation Conversions 4 1. Convert r= into a rectangular equation. 2-sin0 2. Convert 2x - 3y = 5 into a polar equation.arrow_forwardConvert x = 6 to an equation in polar coordinates in terms of r and 0. (Use symbolic notation and fractions where needed.) r =arrow_forwardConvert to an equation in polar coordinates of the form r = f(0).arrow_forward
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