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Generalised energy and energy (lagrangian mechanics)

  1. Jan 12, 2012 #1
    I'm doing lagrangian mechanics and trying to understand my notes, are these three statements correct:

    1. If kinetic energy is quadratic then energy equals generalised energy.
    2. Saying kinetic energy of a system is quadratic is the same as saying none of the position vectors in a system depend explicitly on time.
    3. A lagrangian can be independent of time (generalised energy is conserved) even if kinetic energy is not quadratic (energy DOESN'T equal generalised energy)
     
  2. jcsd
  3. Jan 13, 2012 #2
    Hopefully putting the formulas for generalised energy and energy might help:

    L=T-V (kin-pot)

    generalised energy: h= [itex]\sum\frac{\partial L}{\partial \dot{q}}[/itex][itex]\dot{q}[/itex]-L where [itex]\dot{q}[/itex] should be bold and is the time derivative vector for all generalised coordinates.

    and energy: E=T+V

    Took me about an hour to write out that formula...FAIL.
     
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