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Classical mechanics

  1. Apr 18, 2014 #1
    Ayo everybody, I'm doing a problem about theory of small oscilatons (see pic) and I got the following for potential energy:

    [itex] V= mg(\frac{l_{2}}{2} +\frac{l_{1}}{2} \theta^{2}_{1} + \frac{l_{2}}{4} \theta^{2}_{2}) [/itex] (after the aproximation [itex] cos \theta [/itex]~ [itex]1 - \frac{\theta^{2}}{2} [/itex]

    Knowing that [itex] V = \frac{1}{2} V_{jk} \theta_{jk} [/itex] I need to write the matrix [itex] V_{jk}[/itex]

    Since the term [itex] mg\frac{l_{2}}{2} [/itex] is constant, can I remove it from the potential ?

    And write the matrix like this:

    [itex] V_{jk} =mg \begin{pmatrix}
    l_{1} & 0 \\
    0 & \frac{l_{2}}{2} \\
    \end{pmatrix}
    [/itex]

    If not, how can I remove the constant term?
     

    Attached Files:

    Last edited: Apr 18, 2014
  2. jcsd
  3. Apr 18, 2014 #2

    mfb

    User Avatar
    2016 Award

    Staff: Mentor

    Constant terms don't matter, you can ignore them. They just reflect the arbitrary choice of "zero height".
     
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