Toroidal coordinates (ρ,θ,ψ) are useful in situations in which ... | Filo

Toroidal coordinates (ρ, θ, ψ) are useful in situations in which it is desired to describe movement relative to a reference circle, which is the case for magnetohydrodynamic 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 ρcosψ) cosθ, y=(R ρcosψ) sinθ, z=ρsinψ. Derive expressions for the unit vectors for this coordinate system and for the derivatives of the unit vectors with respect to each t

The sketch defines an orthogonal curvilinear coordinate system ρ, θ, ϕknown as toroidal coordinates. The radius R is a constant parameter on which these coordinates are based. Use the concepts of relative motion to derive the corresponding formulas for velocity and acceleration of point P in terms of the unit vectors of this coordinate system. Figure can't copy | Numerade

Laplace's Equations in Other Coordinates Consider the coordinat... | Filo