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General Information
    • ISSN: 2010-3697
    • Frequency: Bimonthly
    • DOI: 10.7763/IJMO
    • Editor-in-Chief: Prof. Adrian Olaru
    • Executive Editor: Ms.Yoyo Y. Zhou
    • Abstracting/ Indexing: Engineering & Technology Digital Library, ProQuest, Crossref, Electronic Journals Library, Google Scholar, EI (INSPEC, IET).
    • E-mail ijmo@iacsitp.com
Prof. Adrian Olaru
University Politehnica of Bucharest, Romania
I'm happy to take on the position of editor in chief of IJMO. It's a journal that shows promise of becoming a recognized journal in the area of modelling and optimization. I'll work together with the editors to help it progress.
IJMO 2015 Vol.5(3): 198-201 ISSN: 2010-3697
DOI: 10.7763/IJMO.2015.V5.461

Divergence and Curl Operators in Skew Coordinates

Rajai S. Alassar and Mohammed A. Abushoshah
Abstract—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.

Index Terms—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: alassar@kfupm.edu.sa.sa, abushosha@kfupm.edu.sa).


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.

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