CHAPTER 24 - Systems of Orthogonal Coordinates

Abstract

This chapter discusses the systems of orthogonal coordinates. The position vector r of a point in space with the rectangular Cartesian coordinates (x, y, z) can be written r = r( j c , y , z ). The point P with the rectangular Cartesian coordinates (x0, y0, z0) corresponds to the point with the corresponding coordinates in the new coordinate system, and so to the intersection of the three one-parameter curves is defined. Most frequently used systems of orthogonal curvilinear coordinates are given. In each case, the relationship between the curvilinear coordinates and Cartesian coordinates is given together with the scale factors h1, h2, h3, and the forms taken by ∇V, ∇⋅F, ∇× F, and ∇2 V. Bipolar coordinates (u, v, z) are three-dimensional coordinates that shows the coordinate system in the plane z = 0.