Interpretation:
To calculate
Concept Introduction:
The linearized system for
The matrix
Answer to Problem 11E
Solution:
The system in Cartesian coordinate is
The linearized system at the origin is
Explanation of Solution
Using the first equation
Integrating both sides,
When
Solve the stability of the origin by solving
Thus the origin is a stable point.
Solve the nature of the origin by solving
Thus the origin is spiral.
The system in
Comparing the above polar coordinates with the given coordinates,
Multiply equation 1) by x and equation 2) by y and subtract,
Multiply equation 1) by y and equation 2) by x and add,
The Jacobian matrix at any fixed point
Substituting values of
It is proved and origin is a stable star for the linearized system.
Integrating given polar equations we can find
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Chapter 6 Solutions
Nonlinear Dynamics and Chaos
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- Algebra & Trigonometry with Analytic GeometryAlgebraISBN:9781133382119Author:SwokowskiPublisher:Cengage