# Pendulum with Pivot Moving in Horizontal Circle

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1. Nov 12, 2015

### tomdodd4598

The problem statement, all variables and given/known data
The problem is the following: Using a Lagrangian, find the equations of motion of a mass hanging from a massless string, with the pendulum pivot moving in a horizontal circle at constant angular velocity. I take the mass to be m, the length of the string L, the radius of the circle the pivot traces R and the angular velocity ω.

The attempt at a solution
I believe I am capable of finding the Lagrangian and solving the E-L equations, but I am stuck at defining the coordinates of the mass - it surely needs to be related to the moving pivot but am not sure how, and also don't know which coordinate system I should use.

2. Nov 12, 2015

### Staff: Mentor

You can choose any coordinate system you like. Some choices might be easier than others. It is probably useful to have the coordinate system centered at the center of the circle, for example.
The pendulum has two degrees of freedom that you can parametrize.

3. Nov 21, 2015

### tomdodd4598

I think I have found a coordinate system which will work, but I'm still not sure - here is a diagram and the Cartesian coordinates in terms of my chosen parameters (V is the potential energy so don't worry about that):

Are these valid (I ask because I am a little unsure about the cos/sin ωt terms in the second parts of the x and y transformations)?

4. Nov 21, 2015

### Staff: Mentor

$\theta$ is relative to the x axis? Then you don't need the $\omega t$. Otherwise you have to add the two angles and take the cosine (sine) of the sum.

5. Dec 10, 2015

### tomdodd4598

Ok, finally worked it out, removing the cos/sin ωt on the ends of the x and y coordinates - thanks for the help!

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