- #1
firemarsh
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Homework Statement
A ball is sitting on a frictionless seesaw with no inclination at the beginning, and a constant angular velocity [tex]\phi[/tex]. Find the position of the ball as a function of time
Homework Equations
L=T-V, T=(m[tex]\dot{}x[/tex]2+m[tex]\dot{}y[/tex]2)/2, V=mgy
The Attempt at a Solution
The first problem I run into is the dimension of this system, I thought it was a 1 dimension system at first but then suspect it is 2 dimension.
Anyway I take r (distance from pivot pt. to the ball) and [tex]\theta[/tex] as the generalized coordinates.
So I have x=rcos[tex]\theta[/tex], y=rsin[tex]\theta[/tex], which makes T=m([tex]\dot{}r[/tex]2+[tex]\dot{}\theta[/tex]2r2, and V=mglsin[tex]\theta[/tex], and results in Lagrangian:
L=m([tex]\dot{}r[/tex]2+[tex]\dot{}\theta[/tex]2r2-mglsin[tex]\theta[/tex]
obviously [tex]\dot{}\theta[/tex] is the constant [tex]\phi[/tex], so...I am confused right here, how do I continue?