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Appendix A
Curvilinear Coordinate Systems

In the following, we note X = (x,y,z) the vector position in the space under consideration. In general, vectors are written in bold characters, except unit vectors, noted with a hat. We consider the following curvilinear coordinate systems

 A.1 General Case (u1,u2,u3)
  A.1.1 Vector Algebra
  A.1.2 Tensor Algebra
 A.2 Configuration space
  A.2.1 System (R,Z,ϕ)
  A.2.2 System (r,θ,ϕ)
  A.2.3 System (ψ,s,ϕ)
  A.2.4 System (ψ,θ,ϕ)
 A.3 Momentum Space
  A.3.1 System ( p∥,p⊥,φ)
  A.3.2 System (p,ξ,φ)

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