Contemporary physics students are fortunate to have many high-quality, legal resources:
Euler-Lagrange: [ \frac{d}{dt} \left( \frac{\partial L}{\partial \dot{r}} \right) = \frac{\partial L}{\partial r} ] [ \frac{\partial L}{\partial \dot{r}} = m (1 + k^2 r^2) \dot{r} ] [ \frac{d}{dt} \left( \frac{\partial L}{\partial \dot{r}} \right) = m (1 + k^2 r^2) \ddot{r} + 2 m k^2 r \dot{r}^2 ] [ \frac{\partial L}{\partial r} = m k^2 r \dot{r}^2 + m r (\omega^2 - gk) ] Contemporary physics students are fortunate to have many
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