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Conservation and symmetry 
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#1
May107, 10:57 PM

P: 511

I do not know the Lagrangian or Hamiltonian principles of mechanics. However,I came to know that conservation of linear momentum,angular momentum and conservaton of energy lead to homogeneity of space,isotropy of space and homogeneity of time.Can anyone show why it is in purely Newtonian terms?I am familiar with virtual work methods...Otherwise if these conservation laws can be proved from the symmetry principles?You may also refer me to some link.



#2
May207, 02:09 AM

P: 1,235

It is the other way around ...
A symmetry leads to a conservation law, this is called the Noether theorem. It is more general than Newtoniam mechanics. The virtual work method is the origin of Lagragian mechanics. So indeed, it should be possible to explain it on this basis, but this is not usual. Google for Noether, maybe you will find the connections you need. Intuitively, this theorem is very clear. Think to a freely spinning object for example: no force break the symmetry around the rotation axis. If some force would define a preffered position for the spinning object, the angular momentum would not be conserved any more. 


#3
May207, 03:04 AM

P: 511

Thank you for your help.



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