I cant't figure out how to transform ##\dot{r}##, ##\dot{\theta}##, ##\dot{\phi}## in spherical coordinates to ##\dot{x}##, ##\dot{y}##, ##\dot{z}## in cartesian coordinates (the dot is Newton's notation for the first time-derivative which is the angular velocity and velocity).(adsbygoogle = window.adsbygoogle || []).push({});

I have no trouble transforming the coordinates, but if I try ##\sqrt{\dot{r}^2+(\dot{\theta} r)^2+(\dot{\phi} r)^2}## I get the wrong total velocity if adding up the components by Pythagoras. Any ideas why this doesn't work, and even more important, how it works instead?

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# B Velocity transformation from spherical to cartesian coords

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