Lagrangians and conserved quantities

  1. Feb 23, 2010 #1
    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?
     
  2. jcsd
  3. Feb 23, 2010 #2
    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...
     
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