b) Consider again the ODE introduced in point (a) and describing the motion of the pendulum ml0 = -mg sin 0 – y0. with 0 E(-x/2, /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

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter9: Systems Of Equations And Inequalities
Section9.7: The Inverse Of A Matrix
Problem 31E
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b) Consider again the ODE introduced in point (a) and describing the motion of the pendulum
me ð = -mg sin 0 – yð.
with 0 E(-x2, 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
Transcribed Image Text:b) Consider again the ODE introduced in point (a) and describing the motion of the pendulum me ð = -mg sin 0 – yð. with 0 E(-x2, 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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