I don't know for sure if the expressions I want exist. The thing is that the condition depends on both $\delta \theta$ and $\delta \phi$ and I don't know how to derive it.īoth $\delta \theta$ and $\delta \phi$ may be assumed to be very small angles. I've tried to rewrite the epxression to some conditional that checks if $d(x) < 0$, and if so it sums $\pi$ to $\tan(c(x),d(x))$. $$\psi = \arctan2 \left ( -m_y \cos(\phi + \delta \phi) + m_z \sin(\phi + \delta \phi) \, \ m_x \cos(\theta + \delta \theta) + m_y \sin(\psi + \delta \psi) \sin(\theta + \delta \theta) + m_x \cos(\phi + \delta \phi) \sin(\theta + \delta \theta) \right )$$ To be more especific, my equation looks like this: I've searched wherever I've could and the only thing I've come across are the partial derivatives of $\arctan2(y,x)$ with respect to $x$ and $y$. I'm currently working on some navigation equations and I would like to write down the derivative with respect to $x$ of something like $$f(x) = \arctan2(c(x), d(x))$$
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