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Problem with Lagrange's Equations of Motion

  1. Jun 26, 2014 #1

    I have seen some pretty esoteric questions get answered pretty clearly on here so I figured I would give it a shot.

    I am trying to verify a derivation using Lagrange's EOM for a dynamic system and I have run into a snag with one of the terms.

    $$ \frac{d}{dt}(\frac{\partial T}{\partial{\dot {\xi_F}}}) - (\frac{\partial T} {\partial{\xi_F}}) + (\frac{\partial U} {\partial{\xi_F}}) = Q_F $$
    where $$ T= \frac{1}{2}m\mathbf{V}^T\mathbf{V}+\frac{1}{2}\mathbf{\omega}^T\mathbf{\omega} $$ and $$ V=\begin{bmatrix}u & v & w\end{bmatrix}^T $$
    and $$ U=-m g_0 \frac{R_{earth}^2}{R}$$ and last but not least $$ \xi = \begin{bmatrix}R_x & R_y & R_z \end{bmatrix}^T $$

    I am running into issues with taking the derivatives of the scalar relations with respect to the vectors. I think I have the solution but it is looking more complicated then the one I am checking which has me doubting my work.

    I would appreciate any help and I am glad to join the community.
    Last edited: Jun 26, 2014
  2. jcsd
  3. Jul 2, 2014 #2
    I'm sorry you are not generating any responses at the moment. Is there any additional information you can share with us? Any new findings?
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