anonymous
  • anonymous
ques
Mathematics
chestercat
  • chestercat
I got my questions answered at brainly.com in under 10 minutes. Go to brainly.com now for free help!
At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus. Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.

Get this expert

answer on brainly

SEE EXPERT ANSWER

Get your free account and access expert answers to this
and thousands of other questions

anonymous
  • anonymous
In 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 \[\vec r=uv^2w \hat e_{1}+uvw^3 \hat e_{2}+uvw \hat e_{3}\]
anonymous
  • anonymous
@IrishBoy123
IrishBoy123
  • IrishBoy123
@Empty

Looking for something else?

Not the answer you are looking for? Search for more explanations.