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If for a curve in Cartesian coordinates ##||\dot{{\mathbf r}}||=\mbox{const}## (i.e. the curve is constant speed) will the speed of the curve change in cylindrical and spherical coordinates?

Could someone experienced share how the transition from flat Euclidian space to curved space alters the speed of the curve?

Thanks!

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# The speed of a curve in different coordinate systems

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