Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Problem with Lagrange's Equations of Motion

  1. Jun 26, 2014 #1
    Hello,

    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?
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: Problem with Lagrange's Equations of Motion
  1. Euler-Lagrange Equation (Replies: 11)

Loading...