Curvilinear coordinate systems in continuum mechanics

Abstract

The article examines curvilinear coordinate systems generalized from rectangular linear coordinate systems and transformations theirbetween. The theory is based on the theory of linear coordinate systems. Unambigious definition of the base system of linear coordinate systems is considered a key feature of the generalization. The applications concern important coordinate systems applied in continuum mechanics, transformations between the coordinate systems, change of basis, the derivatives of changed bases, and the so-called Christoffel symbols needed in the derivatives. Also benefits of curvilinear coordinates and their transformations are discussed. The article is based on T. Salmi's unpublished written material.