EXERCISE 2.37 Toroidal coordinates (p, 0, ) are useful in situations in which it is desired...

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EXERCISE 2.37 Toroidal coordinates (p, 0, ) are useful in situations in which it is desired to describe movement relative to a reference circle, which is the case for mag- netohydrodynamic studies in the fusion reactor known as a tokamak. Let R be the radius of this reference circle. Then the transformation to Cartesian coordinates is x = (R+ p cos) cos 0, y = (R+ p cos ) sin 0, z = p sin. Derive expressions for the unit vectors for this coordinate system and for the derivatives of the unit vectors with respect to each toroidal coordinate. Then obtain the toroidal coordinate expressions for velocity and acceleration. R -0 Exercise 2.37 EXERCISE 2.37 Toroidal coordinates (p, 0, ) are useful in situations in which it is desired to describe movement relative to a reference circle, which is the case for mag- netohydrodynamic studies in the fusion reactor known as a tokamak. Let R be the radius of this reference circle. Then the transformation to Cartesian coordinates is x = (R+ p cos) cos 0, y = (R+ p cos ) sin 0, z = p sin. Derive expressions for the unit vectors for this coordinate system and for the derivatives of the unit vectors with respect to each toroidal coordinate. Then obtain the toroidal coordinate expressions for velocity and acceleration. R -0 Exercise 2.37

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given toroidal coordinates rho psi R theta X R rhocospsi costheta y R rhocospsisintheta z rhosinphi ... View the full answer