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How can I linearize the following function, where my variables are $\phi_d$, $\dot{\phi_d}$ and $\dot{L}_1$:

$\dot{L}_1=\frac{1}{2\sqrt{(l_d\cos{\phi_d}-x_Q)^2+(l_d\sin{\phi_d}-x_Q)^2-R_2^2}}\small(2((l_d\cos{\phi_d}-x_Q)(-l_d\sin{\phi_d})+(l_d\sin{\phi_d}-y_Q)(l_d\cos{\phi_d})))\dot{\phi}_d$

Thank you

Moreover, I would like to get an example of linearization around the working point: $\phi_d=\frac{3}{2}\pi$, $\dot{\phi_d}=0$ and $\dot{L}_1=0$

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