Register to reply

Lagrangians and conserved quantities

by quasar_4
Tags: conserved, lagrangians, quantities
Share this thread:
quasar_4
#1
Feb23-10, 08:10 PM
P: 290
Hi,

I have a relatively straight forward question. If we have a Lagrangian that only depends on time and the position coordinate (and its derivative), how can I decide whether angular momentum is conserved?

That is, if the Lagrangian specifically does not have theta or phi dependence, does that mean that angular momentum is always conserved?
Phys.Org News Partner Physics news on Phys.org
'Comb on a chip' powers new atomic clock design
Quantum leap in lasers brightens future for quantum computing
Enhanced NIST instrument enables high-speed chemical imaging of tissues
jfy4
#2
Feb23-10, 10:30 PM
jfy4's Avatar
P: 647
I think this is a really good question! I haven't thought of this before until now.

I imagine it would be a little weird for you to be interested in a situation with angular symmetry and not using [tex]\theta[/tex] or [tex]\phi[/tex] and their derivatives for your q and q dot things, but i guess its possible.

Here is my best stab, and im pretty sure of the strength of this statement: Anytime there is a conservation law, it means there is a symmetry in any one of the 4 spatial coordinates. Conservation laws are geometrically based, so look at your system, and if there is a symmetry in one of the coordinates, then there is conservation of something.


I hope this helps...


Register to reply

Related Discussions
Conserved quantities for geodesics Advanced Physics Homework 0
Conserved Quantities in de Sitter ST Advanced Physics Homework 2
Symmetries and conserved quantities Quantum Physics 6
Potential conserved quantities Advanced Physics Homework 5