The velocity of a particle at position r = (x, y), in two-dimensional Cartesian coordinates, is given by v = (αy,αx), where α ∈ R is a constant. What are the physical dimensions of the parameter α? Find the general form of r(t), the position of the particle, as a function of time t (hint: write v = (αy,αx) as a system of first order ODEs). What is the critical point and its nature in this system? Suppose at t = 0, r(0) = (2,0). By eliminating the variable t, find the nature of the particle’s trajectory and give a sketch of it.
The velocity of a particle at position r = (x, y), in two-dimensional Cartesian coordinates, is given by v = (αy,αx), where α ∈ R is a constant. What are the physical dimensions of the parameter α? Find the general form of r(t), the position of the particle, as a function of time t (hint: write v = (αy,αx) as a system of first order ODEs). What is the critical point and its nature in this system? Suppose at t = 0, r(0) = (2,0). By eliminating the variable t, find the nature of the particle’s trajectory and give a sketch of it.
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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The velocity of a particle at position r = (x, y), in two-dimensional Cartesian coordinates, is given by v = (αy,αx), where α ∈ R is a constant. What are the physical dimensions of the parameter α? Find the general form of r(t), the position of the particle, as a function of time t (hint: write v = (αy,αx) as a system of first order ODEs). What is the critical point and its nature in this system? Suppose at t = 0, r(0) = (2,0). By eliminating the variable t, find the nature of the particle’s trajectory and give a sketch of it.
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