Recently I've been studying about orthogonal coordinate systems and vector operations in different coordinate systems.In my studies,I realized there are some inconsistencies between different sources which I can't resolve.(adsbygoogle = window.adsbygoogle || []).push({});

For example in Arfken,it is said that the determinant definition of the cross product is reserved after changing to a coordinate system other than Cartesian and also Foundations of the Electromagnetic theory by Reitz and Milford uses the same way for calculating a cross product in spherical coordinates as in the Cartesian system.

But in documents I found on the internet,the cross product in other coordinate systems involves the [itex] h_i(=\sqrt{g_{ii}}) [/itex] coefficients.One example is here.

But again,the calculations presented in some other documents(like this and this) are that much different in(maybe)notation that I have problem relating them.

I wanna ask,is there a book which is considered as the ultimate reference that its notations and definitions are most widely used?

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# Orthogonal coordinate systems

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