Answered: dz dt dp dt = 2x - z² - p dzz-d= dz

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Advanced Math

dz dt dp dt = 2x - z² - p dzz-d= dz

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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Question

Find the 4 equilibrium points and linearize the system (compute eigenvalues for the system)

dz
dt
dp
dt
2z
2x
- x² - xp
x2
= p² - z²p

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Step 1: Introduction

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Step 2: Calculating Equilibrium points

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Step 3: Linearization of system of differential equation at (0,0) and (2,0)

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Step 4: Linearization of system of differential equation at (1,1) and (-2,4)

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Follow-up Question

What is the stability of the 4 equilibrium points? Does point (0,0) even count?

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