—The divergence and curl operators appear in numerous differential equations governing engineering and physics problems. These operators, whose forms are well known in general orthogonal coordinates systems, assume different casts in different systems. In certain instances, one needs to custom-make a coordinates system that my turn out to be skew (i.e. not orthogonal). Of course, the known formulas for the divergence and curl operators in orthogonal coordinates are not useful in such cases, and one needs to derive their counterparts in skew systems. In this note, we derive two formulas for the divergence and curl operators in a general coordinates system, whether orthogonal or not. These formulas generalize the well known and widely used relations for orthogonal coordinates systems. In the process, we define an orthogonality indicator whose value ranges between zero and unity.
—Coordinates systems, curl, divergence, Laplace, skew systems.
The authors are with the Department of Math and Stat, King Fahd University of Petroleum & Minerals, Dhahran, Saudi Arabia (e-mail: firstname.lastname@example.org, email@example.com).
Cite: Rajai S. Alassar and Mohammed A. Abushoshah, "Divergence and Curl Operators in Skew Coordinates," International Journal of Modeling and Optimization vol. 5, no. 3, pp. 15-21, 2015.