 #1
satanikoskioftes
 10
 2
 Homework Statement:

Test stokes theorem on v(s,φ,z)=(ssinφ)S2zΦ+(2zssinφ)Ζ
My given surface has those points as x,y,z coordinates (0.0.2) (0.0.0) (2.2.0)
Its basically a triangle that one side is on the z axis, the other one is on the xy (x=y). The rotation is counterclockwise
Test stokes theorem on v(s,φ,z)=s(2+sinφ)S(ssinφcosφ)Φ+3zΖ
My given surface has those points as x,y,z coordinates (0.0.3) (2.0.3) (2.2.3)
So its another triangle
capital letter are vectors
 Relevant Equations:
 ∫(∇×F)da=∮F⋅dl
To be honest i don't know from where to start. I know how i can test the stokes theorem if i have a cylindrical shape and a cylindrical vector or spherical vector and a spherical shape but here I am out of ideals.
The first thing i tried was to compute the left part of the stokes theorem but i don't know how to compute the da part
My second attempt was to covert my cylindrical coordinates to x,y,z. If i do that i get some pretty weird integrals though and i don't think that this is the smartest way.
So i think my two main problems are:
1) How to find the da
2) How to express my xyz lines of the triangles to cylindrical moves and use them for my fdl parts
The first thing i tried was to compute the left part of the stokes theorem but i don't know how to compute the da part
My second attempt was to covert my cylindrical coordinates to x,y,z. If i do that i get some pretty weird integrals though and i don't think that this is the smartest way.
So i think my two main problems are:
1) How to find the da
2) How to express my xyz lines of the triangles to cylindrical moves and use them for my fdl parts