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anonymous
 one year ago
ques
anonymous
 one year ago
ques

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anonymous
 one year ago
Best ResponseYou've already chosen the best response.0In an orthogonal curvilinear coordinate system (u,v,w,) We have the scalar factors \[h_{1}=\frac{\partial \vec r}{\partial u} \space ; \space h_{2}=\frac{\partial \vec r}{\partial v}\space ; \space h_{3}=\frac{\partial \vec r}{\partial w}\] Are these factors constant or they vary with u,v,w?? Because in case of cartesian coordinate system where we have \[\vec r=x \hat i+y \hat j+z \hat k\]\[\frac{\partial \vec r}{\partial x}=1 \space ; \space \frac{\partial \vec r}{\partial y}=1 \space ; \space \frac{\partial \vec r}{\partial z}=1\] \[\vec r=X(x,y,z)\hat i+Y(x,y,z)\hat j+Z(x,y,z) \hat k\] Are the cartesian coordinates "a special case" where \[X(x,y,z)=x \space ; \space Y(x,y,z)=y \space ; \space Z(x,y,z)=Z \space ; \space\] The 3 functions are just in fact single variable and simple because in some orthgonal curvilinear system we may have \[\vec r=X(u,v,w)\hat e_{1}+Y(u,v,w)\hat e_{2}+Z(u,v,w) \hat e_{3}\] Now this can be something like \[\vec r=uv^2w \hat e_{1}+uvw^3 \hat e_{2}+uvw \hat e_{3}\]
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