1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Trajectory plotting.

  1. Nov 12, 2012 #1
    Hello,

    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:
    t=0:0.1:10
    x=t-sin(t)
    y=1-cos(t)
    plot(x,y)
     
  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?
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: Trajectory plotting.
  1. Trajectory of a ball (Replies: 1)

  2. Projectile trajectories (Replies: 21)

  3. Trajectory lab (Replies: 13)

Loading...