Can someone check my Lagrangian ?

  • Thread starter kala
  • Start date
  • #1
21
0

Homework Statement


Write down the Lagrangian for a cylinder mass m, radius R an moment of inertia I, that rolls without slipping straight down an inclined plane which is at an angle a from the horizontal. Use as your generalized coordinate the cylinder's distance x measure down the plane from its starting point. Write down the Lagrange equation and solve it for the cylinder's acceleration.





The Attempt at a Solution


I tried to find the Lagrangian, this is what i have so far, is it right?
i said that T=1/2mv2+1/2Iw2
and U= -mgxsina so my Lagrangian would be
L=1/2mv2+1/2Iw2+mgxsina.
I think this is correct, but I'm not positive. If it is right then should i write I and w (omega) differently? and then continue with the partial differentiation?
 

Answers and Replies

  • #2
207
1
Everything is correct, except that you must express all the dynamical variables (v, w) in terms of x and its derivatives, as the problem tells you. Also you can explicitly specify the value for I, since you know the shape of the body.
 
  • #3
12
0
so if i remember right v=x' but i am not sure what I and w are in terms of x and derivatives. doesn't I have something to do with R, the radius?
 
  • #4
207
1
w is the angular velocity, which for non-slipping case is given by

[tex]\omega = \frac{v}{R} = \frac{\dot{x}}{R}[/tex]

and I hope you can figure out the moment of inertia I yourself.
 
  • #5
12
0
I= 1/2 m R2?
Just checking before I go on with the partial derivatives.
 
  • #6
207
1
Yes, for a uniformly filled cylinder.
 

Related Threads on Can someone check my Lagrangian ?

  • Last Post
Replies
1
Views
1K
Replies
2
Views
2K
  • Last Post
Replies
3
Views
1K
Replies
3
Views
1K
  • Last Post
Replies
2
Views
1K
Replies
0
Views
1K
  • Last Post
Replies
5
Views
4K
  • Last Post
Replies
5
Views
2K
Top