- #1

Istiak

- 158

- 12

- Homework Statement
- Find equation of motion of a incline plane when there's friction using Lagrangian

- Relevant Equations
- L=T-V ##\frac{d}{dt}(\frac{\partial L}{\partial \dot{x}})-\frac{\partial L}{\partial x}+\frac{\partial f}{\partial \dot{x}}=0##

It's the body. So there's friction on that plane and there's tension also.

$$L=\frac{1}{2}m_1\dot{x}^2+\frac{1}{2}m_2\dot{x}^2-m_2g(l-x)-m_1gx\sin\theta$$

$$f=\mu N=-\mu m_1 g\dot{x}\cos\theta$$

I had found the frictional force's equation from [the class](https://www.youtube.com/watch?v=5UE9kzVcFao).

Using Euler Lagrange :

$$m_1\ddot{x}+m_2\ddot{x}-m_g+m_1g\sin\theta-\mu m_1 g\cos\theta=0$$

After rearranging the equation :

$$\ddot{x}=\frac{m_2+\mu m_1\cos\theta-m_1\sin\theta}{m_1+m_2}g$$

But my book says little bit different thing (only differences in sign) I had tried by taking negative common. Although my answer didn't match. Why?