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Trajectory plotting. 
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#1
Nov1212, 11:52 AM

P: 818

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
Nov1212, 12:00 PM

P: 286

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=tsin(t) y=1cos(t) plot(x,y) 


#3
Nov1212, 12:01 PM

P: 818

I am not supposed to use any program, simply infer the general scheme of the trajectory from the equations. Any ideas?



#4
Nov1212, 12:36 PM

P: 286

Trajectory plotting.
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 yvalue is moved up by R? You simply translate your circle. Then, what happens if every xvalue is moved right by Rt? It will not be a circle anymore. For instance, the endpoint at t=2*pi (when w=1) will have moved to x=R*2*pi. You can take one or two other tvalues to get the shape. I have taken w=1, but it is easy to generalize the above approach. 


#5
Nov1212, 02:16 PM

P: 818

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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