- #1
Dustinsfl
- 2,281
- 5
Homework Statement
The system can pivot at point O and I am taking small angle approximations.
I am trying to determine the Lagrangian, ##\mathcal{L} = T - U## for the following system:
Homework Equations
E-L equation with dissipation: ##\frac{\partial\mathcal{L}}{\partial q_i} - \frac{d}{dt}\frac{\partial\mathcal{L}}{\partial\dot{q}_i} + \frac{\partial D}{\partial\dot{q}_j} = 0##
The Attempt at a Solution
I am going to use the generalized coordinate theta.
For the circular mass, I have the potential energy to be ##mg(1-\cos(\theta)) = \frac{mg\theta^2}{2}## and the kinetic energy is ##\frac{1}{2}J\dot{\theta}^2## where J is the mass moment of inertia. The potential energy of the spring is ##\frac{1}{2}kx^2##, and the dissipative energy is ##D = c\frac{\dot{x}^2}{2}##.
Before I convert the xs to thetas am I missing a kinetic or potential energy?