Physical interpretation of invariance of vector differential operators in three orthogonal coordinate systems and a case study of wall and globe of death

Author:

Gapale D LORCID,Arote S AORCID,Baviskar P KORCID,Navale S R,Palve B MORCID,Bardapurkar P PORCID,Pathan A S,Dalvi S N

Abstract

Abstract In the present study, the effect of operators on fundamental physical quantities in three orthogonal coordinate systems was analyzed using differential equations. The mathematical expression for the position vector and its magnitude, velocity, &acceleration in three orthogonal coordinate systems were obtained from the geometry of the figure and differentiation. The derivations of operation of vector differential operators (curl and diversions) on position vectors were derived, and their physical significance was illustrated. Similarly, the operation of the Laplacian operator on the magnitude of the position vector was also studied. The study highlighted the invariance in the results of all operations in three orthogonal coordinate systems. An investigation has been performed to describe the wall of death and the globe of death problem in appropriate orthogonal coordinate systems. The interpretations in terms of velocity, acceleration, and the net force acting on the vehicle are explained in detail.

Publisher

IOP Publishing

Reference13 articles.

1. NURBS surface fitting using orthogonal coordinate transform for rapid product development;Bae;Comput. Aided Des.,2002

2. Electric vector potential formulation in electrostatics: analytical treatment of the gaped surface electrode;Salazar;Eur. Phys. J. Plus.,2020

3. The hydrogen atom according to wave mechanics - I. spherical polar coordinates;Ogilvie;Cienc. Tecnol.,2016

4. Benchmark values of Shannon entropy for spherically confined hydrogen atom;Jiao;Int. J. Quantum Chem.,2017

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