 #1
Istiak
 158
 10
 Homework Statement:
 Find equation of motion using Lagrangian of Atwood machine
 Relevant Equations:

L=TU
##\frac{d}{dt}(\frac{\partial L}{\partial \dot{q}})=\frac{\partial L}{\partial q}##
I could see there's 3 tension in 2 body. Even I had seen 2 tension in a body. It was little bit confusing to me. I could find tension in Lagrangian from right side. But left side was confusing to me.
$$L=\frac{1}{2}m_1\dot{x}^2+\frac{1}{2}m_2\dot{x}^2$m_1gxm_2g(lx)m_2g(l_1x)$$
Here $lx$ is representing the potential energy for "center rope" tension and l_1x is representing tension for right one.
After using Euler form and rearranging I get that
$$\ddot{x}=\frac{2m_2m_1}{m_1+m_2}g$$
I don't know if the answer is correct. I know that the acceleration is for whole body. But in the book, they had found separated acceleration
From their equation it's like actually my answer is wrong.