Abstract
This chapter focuses on the systems of orthogonal coordinates. The chapter reviews the curvilinear coordinates and discusses vector operators in orthogonal coordinates. The chapter discusses the most frequently used systems of orthogonal curvilinear coordinates. In each case the relationship between the curvilinear coordinates and the Cartesian coordinates is given. Also, the rectangular Cartesian coordinates, the cylindrical polar coordinates, the spherical coordinates, the bipolar coordinates, and the toroidal coordinates are discussed. The toroidal coordinates are three-dimensional coordinates defined in terms of two-dimensional bipolar coordinates. The parabolic cylindrical coordinates, paraboloidal coordinates, elliptic cylindrical coordinates, prolate spheroidal coordinates, and the oblate spheroidal coordinates are also reviewed. The paraboloidal coordinates are three-dimensional coordinates defined in terms of two-dimensional parabolic cylindrical coordinates. The prolate spheroidal coordinates are three-dimensional coordinates defined in terms of two-dimensional elliptic cylindrical coordinates.
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