Consider a point particle with position vector r = (x, y, z) in Cartesian coordinates, moving with a velocity v = (β, αz, −αy), where α and β are positive constants. Find the general form of r(t), the position of the particle, as a function of time t, (hint: write v = (β, αz, −αy) as a system of first order ODEs and note that the equation for x is decoupled from the others). Describe in words the motion of the particle and sketch its trajectory in R3 (you can use software packages for the plot).
Consider a point particle with position vector r = (x, y, z) in Cartesian coordinates, moving with a velocity v = (β, αz, −αy), where α and β are positive constants. Find the general form of r(t), the position of the particle, as a function of time t, (hint: write v = (β, αz, −αy) as a system of first order ODEs and note that the equation for x is decoupled from the others). Describe in words the motion of the particle and sketch its trajectory in R3 (you can use software packages for the plot).
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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Consider a point particle with position
Find the general form of r(t), the position of the particle, as a function of time t, (hint: write v = (β, αz, −αy) as a system of first order ODEs and note that the equation for x is decoupled from the others). Describe in words the motion of the particle and sketch its trajectory in R3 (you can use software packages for the plot).
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