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Homework Help: Vector analysis: show the object moves on the elliptical path

  1. May 24, 2014 #1
    1. The problem statement, all variables and given/known data
    problem form div curl grad and all that by h.m.schey
    An object moves in xy-plane in such a way that its position vector r is given as a some function of "t" by

    r= i acosωt+j bsinωt

    show the object moves on the elliptical path
    2. Relevant equations

    3. The attempt at a solution
    I tried the problem by changing cosωt=x and sinωt=y but i dont know how to proceed further, i dont know how to eliminate the unit vectors i, j. help me. Thank you
    Last edited: May 24, 2014
  2. jcsd
  3. May 24, 2014 #2


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    Gold Member

    You have to show that for the given parametrisation of the coordinates ##x(t)## and ##y(t)##, the equation for an ellipse is satisfied, that equation being the one you wrote in Relevant equations. What is x(t) and y(t) in this case?
  4. May 24, 2014 #3


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    Science Advisor

    Well, that's your first error. It should be x= a cos(ωt), y= b sin(ωt) so that x/a= cos(ωt), y/b= sin(ωt). Now use the fact that sin^2+ cos^2= 1.

    ?? There are no vectors in your equation for x and y as functions of t!
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