- #1
Kelly Lin
- 29
- 0
Homework Statement
Homework Equations
The Attempt at a Solution
I know we can solve it by letting
[tex]
x=acos(\omega t)+acos(\theta+\omega t)\\
y=asin(\omega t)+asin(\theta +\omega t)
[/tex]
and put their derivatives into the Lagrangian.
But, I want to check the other points of view whether it is wrong or something else is missing.
[tex]
a\dot{\theta} = v_{\text{bead}}-v_{\text{hoop}}\\
v_{\text{bead}} = a\dot{\theta}+ a\omega
[/tex]
Thus, the Lagrangian will be
[tex]
L=\frac{1}{2}m(a\dot{\theta}+ a\omega)^{2}
[/tex]
But, there is a huge difference between two results. Can someone enlighten me? THANKS!