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## Main Question or Discussion Point

I'm a bit confused about parallel transport. We demand that the absolute covariant derivative of our (generalised) coordinates is zero along some curve in some frame. Does this really make our vector stay parallel? What if these coordinates were angles or some other general curvilinear coordinate system?

Now that I think about it, the same can be said about the principle of covariance - why should the equations of motion be the same for angles as they are for regular position coordinates? Obviously I am missing something here...

Now that I think about it, the same can be said about the principle of covariance - why should the equations of motion be the same for angles as they are for regular position coordinates? Obviously I am missing something here...