IIARD International Institute of Academic Research and Development

RESEARCH JOURNAL OF PURE SCIENCE AND TECHNOLOGY (RJPST )

E-ISSN 2579-0536
P-ISSN 2695-2696
VOL. 5 NO. 2 2022
DOI: https://doi.org/10.56201/rjpst.v5.no2.2022.pg30.35

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Parabolic Cylindrical Description of Velocity and Acceleration Tensor in Bipolar Coordinate Using Tensor Analysis

K.O. Emeje, V.O. Obaje & J.F. Omonile

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Abstract

Instantaneous velocity and acceleration are often studied and expressed in Cartesian, Circular Cylindrical, and Spherical Coordinate systems but it is a well-known fact that some bodies cannot be perfectly described in these coordinate systems, so they required some other curvilinear systems such as oblate spheroidal, parabolic cylindrical, elliptic cylindrical bipolar, and others. It is of important interest in theoretical physics to establish equations of motion in Bipolar Coordinate system, which is essentially suitable to accurately describe the motion of bipolar bodies such as hyperbolas, ellipses and other curves in the universe. In this work, we derived a new expression for the instantaneous velocity and acceleration vector of bodies and test particles in the bipolar coordinate system using tensor analysis. The Laplacian of a scalar field in this bipolar coordinate system was also derived which has applications in mechanics.

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References:

Howusu,S.X.K (2003) Vector and Tensor Analysis, University of Jos, Nigeria. ISBN: 978-
166-296-4.

Omonile, J.F., Koffa, D. J., & Howusu, S.X.K. (2014a) Velocity and Acceleration in
Parabolic Coordinate, IOSR Journal of Applied (IOSR-JAP), 6(1), 32-33.

Omonile, J.F., Koffa, D. J., & Howusu, S.X.K. (2014b) Velocity and Acceleration in Prolate
Spheroidal Coordinate. Archives of Physics Research 5(1), 56-59

Omonile, J.F., Koffa, D. J., & Howusu, S.X.K. (2014c) Planetary equations based upon
Newton’s gravitation field of a static homogenous Oblate spheroidal sun. Pelagia
Research Library. Advances in applied science research, 5 (1): 282-287.

Spiegel, M.R. (1974) Theory and problems of Vector Analysis and introduction to Tensor
Analysis. McGraw Hill, New York, 166-217.

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