Problem 6: Consider the following nonlinear differential system: * = -y - a(12 + y²) sin (Va? + 32 ý = = - v(2? + 1*) sin (V+ ). Use the Lyapunov's second method to decide whether the origin (0,0) is a (a). stable critical solution of the above system; (Ъ). Find out all the stable and unstable limit cycles of the system.
Problem 6: Consider the following nonlinear differential system: * = -y - a(12 + y²) sin (Va? + 32 ý = = - v(2? + 1*) sin (V+ ). Use the Lyapunov's second method to decide whether the origin (0,0) is a (a). stable critical solution of the above system; (Ъ). Find out all the stable and unstable limit cycles of the system.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Transcribed Image Text:Problem 6: Consider the following nonlinear differential system:
i = --y - (x? + y?) sin (V? +- 32),
ý = =- v(2? + 1*) sin (V+ g).
Use the Lyapunov's second metliod to decide whether the origin (0,0) is a
(a).
stable critical solution of the above system;
(b).
Find out all the stable and unstable limit cycles of the system.
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