Please drive expressions 6-31, 6-32,6.33, thank you 828SA.7Appendix AVector and Tensor NotationSpherical CoordinatesWe now tabulate for reference the same kind of information for spherical coordinates r.0, 4. These coordinates are shown in Figure A.6-1b. They are related to the Cartesian co-ordinates byCylr = +Vx + y² + z?0 = arctan(Vx + y/z)$ = arctan(y/x)(A.6-22)(A.6-23)(A.6-24)x = r sin 0 cos o(A.6-19)y = r sin 0 sin øz=r cos 0(A.6-20)(A.6-21)For the spherical coordinates we have the following relations for the derivativeoperators:cos 0 cos psin o(A.6-25)= (sin 0 cos b)dxr sin 0) aødrcos o+r sin 0) apcos 0 sin ø(A.6-26)= (sin 0 sin 4)dyare= (cos 0)+drsin 0+ (0)(A.6-27)azThe relations between the unit vectors are8, = ( sin 0 cos )ô, + ( sin 0 sin )ô, +( cos 0)ô-d = ( cos 0 cos )ô̟ + ( cos 0 sin ø)ô, + (– sin 0)§,d = (- sin ø)ô, + ( cos o)ô, + (0)ô,(A.6-28)(A.6-29)(A.6-30)andDnie these& = (sin 0 cos )ô, + ( cos 0 cos )d, + (– sin ø)ôs8, = (sin 0 sin )ô, + (cos 0 sin 4)d, + ( cos 4)ôs8, = ( cos 0)ô, + (– sin 0)d, + (0)8s(A.6-31)(A.6-32)equenlons(A.6-33)And, finally, some sample operations in spherical coordinates are(0:T) = 0„T7+ 0;„Ter + TrdTor(A.6-34)u, ug(u·[v X w]) = v,(A.6-35)w, We WoThat is, the relations (not involving V!) given in SSA.2 and 3 can be written directly interms of spherical components.

Name: Please drive expressions 6-31, 6-32,6.33, thank you 828SA.7Appendix AV
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Description: Please drive expressions 6-31, 6-32,6.33, thank you 828SA.7Appendix AVector and Tensor NotationSpherical CoordinatesWe now tabulate for reference the same kind of information for spherical coordinates r.0, 4. These coordinates are shown in Figure A.6