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Finding Conserved Quantities of a Given Lagrangian

  1. Feb 19, 2013 #1
    1. The problem statement, all variables and given/known data
    Find two independent conserved quantities for a system with Lagrangian

    [tex] L = A\dot{q}^{2}_{1} + B\dot{q_{1}}\dot{q_{2}} + C\dot{q}^{2}_{2} - D(2q_{1}-q_{2})^{4}\dot{q_{2}} [/tex]

    where A, B, C, and D are constants.

    2. Relevant equations
    None.


    3. The attempt at a solution
    I've only found one symmetry,

    [tex] q_{1}\rightarrow q_{1}+C [/tex]
    [tex] q_{2}\rightarrow q_{2}+2C [/tex]

    with the corresponding conserved quantity

    [tex] 2\dot{q_{1}}(A+B) + (B+4C)\dot{q_{2}} - 2D(2\dot{q_{1}}-\dot{q_2})^{4} [/tex]

    The other symmetry and conserved quantity is not so obvious to me.

    This is actually a homework assignment I got back and am looking over for a test.
     
    Last edited: Feb 19, 2013
  2. jcsd
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