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Trajectory plotting.

by peripatein
Tags: plotting, trajectory
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peripatein
#1
Nov12-12, 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?
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bigfooted
#2
Nov12-12, 12:00 PM
P: 288
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)
peripatein
#3
Nov12-12, 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?

bigfooted
#4
Nov12-12, 12:36 PM
P: 288
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 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.
peripatein
#5
Nov12-12, 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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