# Problem with Lagrange's Equations of Motion

1. Jun 26, 2014

### Pelfaid

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. Jul 2, 2014