Complex formulation of classical mechanics

  • Thread starter 2VtQCxn
  • Start date
  • #1
8
0

Main Question or Discussion Point

Looking at a path of system state (x(t),v(t)) as a vector, the Lagrangian strangely is a scalar function of pairs of coordinates of the vector.

If, on the other hand, the complete state of a system was captured in a single complex number x+iv, a complex analogue of the Lagrangian would simply transform a vector R->C into another vector R->C (vaguely reminiscent of the symmetry of Poisson brackets).

Is there a formulation of Lagrangian mechanics that does something like this?
 
Last edited:

Answers and Replies

  • #2
970
3
I'm not sure I understand what R->C means?

I'm pretty sure you can write (x,v) as an imaginary number x+iv. However, you don't really get anything out of it since your Lagrangian will not be analytic, and you'll have two independent variables x+iv and it's conjugate, which is the same as having two variables (x,v).

So I don't think such a formulation gives you anything new.
 
  • #3
A quick search showed me that, no idea how serious it is:\
Complex Elliptic Pendulum
Carl M. Bender, Daniel W. Hook, Karta Kooner
http://arxiv.org/abs/1001.0131
 

Related Threads on Complex formulation of classical mechanics

Replies
1
Views
975
Replies
8
Views
960
Replies
7
Views
5K
  • Last Post
Replies
20
Views
3K
  • Last Post
Replies
9
Views
2K
  • Last Post
Replies
2
Views
1K
  • Last Post
Replies
6
Views
1K
Replies
16
Views
3K
Replies
8
Views
6K
Top