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Homework Help: Trajectory plotting.

  1. Nov 12, 2012 #1

    How may I plot the trajectory of a particle whose movement vectors are given as:
    x(t) = Rwt - Rsin(wt)
    y(t) = R - Rcos(wt)

    I have tried squaring both x and y and adding them, to infer some sort of circular trajectory, to no avail. Could someone please assist/make a suggestion?
  2. jcsd
  3. Nov 12, 2012 #2
    You didn't mention in what plotting program (matlab,scilab, gnuplot) but usually, you need to create a vector of values for time first, then calculate the x and y vectors and plot y against x.
    e.g. in matlab and scilab you do:
  4. Nov 12, 2012 #3
    I am not supposed to use any program, simply infer the general scheme of the trajectory from the equations. Any ideas?
  5. Nov 12, 2012 #4
    OK, then do this:

    start from t=0 to get the starting point (x,y).
    Then, knowing that (x,y)=(-Rsin(t),-Rcos(t)) describes a circle of radius R, what will happen if every y-value is moved up by R? You simply translate your circle.

    Then, what happens if every x-value is moved right by Rt? It will not be a circle anymore. For instance, the end-point at t=2*pi (when w=1) will have moved to x=R*2*pi. You can take one or two other t-values to get the shape.

    I have taken w=1, but it is easy to generalize the above approach.
  6. Nov 12, 2012 #5
    Supposing now that the particle's trajectory is given by at^2+bt, where units of a are m/s^2 and units of b are m/s. How am I to calculate its tangential and centripetal accelerations? I know that the radial acceleration is equal to r*w^2 but what about the tangential acceleration and how is all of that related to the trajectory as given with parameters a and b? Do I simply differentiate twice wrt t?
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