Angular momentum

  • Thread starter Piano man
  • Start date
  • #1
75
0
I've got a question about angular momentum arising from Landau-Lifgarbagez p21.

Firstly, I'm not sure where this equation comes from:

[tex]M_z=\sum_a \frac{\partial L}{\partial \dot{\phi}_a}[/tex]

and from that, how do you get

[tex]M_z=\sum_a m_a(x_a \dot{y}_a-y_a \dot{x}_a)[/tex]

Thanks for any help.
 

Answers and Replies

  • #2
Meir Achuz
Science Advisor
Homework Helper
Gold Member
3,529
112
The partial derivative of the Lagrangian with respect to the time derivative of a space variable is the canonical momentum for that degree of freedom.
The second equation comes from a change of variables from r,phi to x,y.
You may want to study the Lagrangian in a good mechanics book.
 
  • #3
75
0
Ok, I still don't really follow.
When you say 'canonical momentum', is that derived from somewhere or is it empirical?
And I've been trying to change the variables to get the second equation, but I'm not getting anywhere. How does it work?
Thanks for your help.
 

Related Threads on Angular momentum

  • Last Post
Replies
1
Views
927
  • Last Post
Replies
5
Views
2K
  • Last Post
Replies
2
Views
1K
  • Last Post
2
Replies
30
Views
4K
  • Last Post
Replies
3
Views
1K
  • Last Post
Replies
1
Views
2K
  • Last Post
Replies
1
Views
1K
  • Last Post
Replies
1
Views
941
  • Last Post
Replies
1
Views
1K
  • Last Post
Replies
11
Views
2K
Top