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Conserved quantities in mechanics

  1. Oct 25, 2012 #1
    So having been through translation and rotation I can conclude that my book has found 3 conserved quantities in classical dynamics:
    Energy
    Angular momentum
    Momentum
    That is 7 separate quantities which are conserved E,Lx,Ly,Lz,px,py,pz
    But this question is bothering me: How do we know that there are not more conserved quantities?
     
  2. jcsd
  3. Oct 25, 2012 #2
    Conservation laws come from invariance of the Lagrangian with each degree of freedom.
    If you can think of another degree of freedom you can have another conservation law.
     
  4. Oct 25, 2012 #3
    Is momentum always conserved?

    Suppose I direct a hosepipe horizontally at a wall.

    Please explain conservation of horizontal momentum at the wall face in this case.
     
  5. Oct 25, 2012 #4

    mfb

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    In closed systems.

    Some systems have additional conserved quantities, for example the Kepler problem or harmonic oscillators. But in the general case, you just have those 7 conserved quantities.
     
  6. Oct 25, 2012 #5
    @mfb
    Yes it is good to specify the conditions.
    These were not originally specified and mechanics is not exclusively about closed systems, and should not be taught or thought of as such.

    In my career I have seen spectacular failures of mechanical systems due to failure to appreciate this.
     
  7. Oct 25, 2012 #6

    D H

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    Simple. The (effectively) infinitely massive wall moves at an (effectively) infinitesimally small rate. The product mass*velocity is some finite, non-zero quantity that exactly obeys conservation of momentum.
     
  8. Oct 25, 2012 #7
    So where does the perpendicular (to the flow) momentum come from at the wall face?
     
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