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.
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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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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