) Consider again the ODE introduced in point (a) and describing the motion of the pendulum me0=-mg sin 0-10. with 0€ (-x/2, x/2). Put m = 1 and = 1. ● Convert this ODE into a system of two first-order ODES ● Compute all equilibria of this system of ODEs. Linearise this system of ODE around each equilibrium. Find the eigenvalues of the linearised system around each equilibrium
) Consider again the ODE introduced in point (a) and describing the motion of the pendulum me0=-mg sin 0-10. with 0€ (-x/2, x/2). Put m = 1 and = 1. ● Convert this ODE into a system of two first-order ODES ● Compute all equilibria of this system of ODEs. Linearise this system of ODE around each equilibrium. Find the eigenvalues of the linearised system around each equilibrium
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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![b) Consider again the ODE introduced in point (a) and describing the motion of the pendulum
me0= -mg sin 0-10.
with 0 € [-x/2, x/2]. Put m = 1 and = 1.
●
Convert this ODE into a system of two first-order ODES
• Compute all equilibria of this system of ODES. Linearise this system of ODE around each
equilibrium. Find the eigenvalues of the linearised system around each equilibrium](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F0ef4cc44-00f5-4e4f-957e-3112ed5a7b2f%2F79fdc3f6-1ef8-4189-a0b1-72d2e2633236%2Fvtl155h_processed.jpeg&w=3840&q=75)
Transcribed Image Text:b) Consider again the ODE introduced in point (a) and describing the motion of the pendulum
me0= -mg sin 0-10.
with 0 € [-x/2, x/2]. Put m = 1 and = 1.
●
Convert this ODE into a system of two first-order ODES
• Compute all equilibria of this system of ODES. Linearise this system of ODE around each
equilibrium. Find the eigenvalues of the linearised system around each equilibrium
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