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Transforming Lagrangian without changing the equations of motion.

  1. Nov 20, 2011 #1
    I know that it works with adding a total time derivative and multiplying the Lagrangian by a constant.
    are these the only things that can be done to a Lagrangian such that the equations of motion have the same solutions q(t).

  2. jcsd
  3. Nov 20, 2011 #2
    There is a wider class of so called canonical transformations.
  4. Nov 20, 2011 #3
    These are the ones i'm having a problem with. the modified Hamilton's principle gives this definition for a canonical transformation:
    pq - H = PQ - K + (total time derivative).. and that's because you can add a total time derivative inside the integral for the action.
    I also want to know if there is more transformations on the Lagrangian without a change of variables.

    Thanks :)
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