For geotrophic flows in the atmosphere of the Earth, the following first order system of ODE is formulated. X' = AX where 1 0 0 X2 and x= A = 1 X4 The solution vector X relates to the velocities and accelerations of two perpendicular components of airflows tangential to the surface of the Earth. The symbols u and a represent the kinematic viscosity of air and the Coriolis constant; and both of them can be assumed as constants. (i) Find the eigenvalues of the matrix;

For geotrophic flows in the atmosphere of the Earth, the following first order system of ODE is formulated. X' = AX where 1 0 0 X2 and x= A = 1 X4 The solution vector X relates to the velocities and accelerations of two perpendicular components of airflows tangential to the surface of the Earth. The symbols u and a represent the kinematic viscosity of air and the Coriolis constant; and both of them can be assumed as constants. (i) Find the eigenvalues of the matrix;

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter4: Eigenvalues And Eigenvectors

Section4.6: Applications And The Perron-frobenius Theorem

Problem 69EQ: Let x=x(t) be a twice-differentiable function and consider the second order differential equation...

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