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Hamiltonian & Generalised cooordinates

  1. Apr 28, 2010 #1
    1. The problem statement, all variables and given/known data

    Let [tex]T = \frac{1}{2}T_{ij}\dot{q_{i}}\dot{q_{j}}[/tex] and [tex]V = \frac{1}{2}V_{ij}q_{i}q_{j}[/tex]. Verify that the equation of motion [tex]T_{ij}\ddot{q_{j}} + V_{ij}q_{j} = 0[/tex] imply that the energy T + V is conserved. Can the constancy of T+V be used to deduce the equations of motion?

    2. Relevant equations

    non

    3. The attempt at a solution

    Using the product rule, i can show the time derivative of T+V is zero given the equations of motion. But I have to assume T and V are symmetric, is this always true?

    I don't know how to deduce equations of motion from constancy of T+V though.
     
  2. jcsd
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