I Question About Curvilinear Cooridnates

[TonyEsposito]

Hi guys, i can not understand something about curvilnear coordinates...from a "geometric" point of view what dose the componentes of the vector mean? in a non-curvilinear coordinates the components are the "projections" on along the bases but in a curvilinear coordinates the directions of the basis vectors changes from point to pint so i can not grasp the geometrical meaning!
Thanks!

 

[Orodruin]

The components are still the projection on the basis vectors. In general, it only makes sense to talk about the projection on the basis at the same point as the vector is defined and therefore it is not really an issue that the basis changes from point to point.

Of course, if you want to integrate a vector quantity, it does matter - but can be taken into account fairly easy.

 

[TonyEsposito]

Ok...thanks! :)