- #1
Clever-Name
- 380
- 1
So I was debating whether or not to post this in the homework session but I feel the question I'm asking belongs here.
I just worked out a problem for my Classical Mechanics Assignment and while I arrived at the solution I am wonder what 'comment' can be made about the result.
It is from L/L Mechanics, page 12 problem 4.
It asks you to find the Lagrangian for a system that looks like the picture attached that is rotating at a constant angular velocity Omega around the fixed vertical axis.
The Lagrangian comes out to be:
[tex] L = m_{1}a^{2}(\dot{\theta}^{2} + \sin^{2}(\theta)\Omega^{2}) + 2m_{2}a^{2}\sin^{2}(\theta)\dot{\theta}^{2} + 2(m_{1} + m_{2})gacos(\theta) [/tex]
I guess my real question is HOW can you recognize how the system will behave just by looking at the Lagrangian. I realize I could solve the Euler-Lagrange equations and solve for the equation of motion in terms of theta but that isn't what this is asking. I feel like there should be some intuitive description of the system just by looking at the Lagrangian.
Any thoughts?
I just worked out a problem for my Classical Mechanics Assignment and while I arrived at the solution I am wonder what 'comment' can be made about the result.
It is from L/L Mechanics, page 12 problem 4.
It asks you to find the Lagrangian for a system that looks like the picture attached that is rotating at a constant angular velocity Omega around the fixed vertical axis.
The Lagrangian comes out to be:
[tex] L = m_{1}a^{2}(\dot{\theta}^{2} + \sin^{2}(\theta)\Omega^{2}) + 2m_{2}a^{2}\sin^{2}(\theta)\dot{\theta}^{2} + 2(m_{1} + m_{2})gacos(\theta) [/tex]
I guess my real question is HOW can you recognize how the system will behave just by looking at the Lagrangian. I realize I could solve the Euler-Lagrange equations and solve for the equation of motion in terms of theta but that isn't what this is asking. I feel like there should be some intuitive description of the system just by looking at the Lagrangian.
Any thoughts?