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Dissipative Function of Air Drag

  1. Jul 7, 2010 #1
    We have [tex]\dfrac{d}{dt}\left(\dfrac{\partial \mathcal L}{\partial \dot{q}_j}\right)-\dfrac{\partial \mathcal L}{\partial q_j}=-\dfrac{\partial \mathcal F}{\partial \dot{q}_j}[/tex].

    If the force of friction is [tex]F=-kv^2[/tex] how do you go about calculating [tex]\mathcal F[/tex]

    My idea is as follows

    [tex]F=-kv^2 \dfrac{\textbf{v}}{|\textbf{v}|}[/tex]

    In 2D we have



    And the Lagrange equations become

    [tex]\dfrac{d}{dt}\left(\dfrac{\partial\mathcal{L}}{\partial\dot{q}_{j}}\right)-\dfrac{\partial\mathcal{L}}{\partial q_{j}}=-k\dot{q}_{j}\sqrt{\sum_{i=1}^{n}\dot{q}_{i}^{2}}[/tex]

    Is this correct?
    Last edited: Jul 8, 2010
  2. jcsd
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