Physical interpretation of invariance of vector differential operators in three orthogonal coordinate systems and a case study of wall and globe of death
Year: 2024
Type: article
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.
Source: Physica Scripta
Institution: Savitribai Phule Pune University
Language: English
Subfield: Modeling and Simulation
Field: Mathematics
Domain: Physical Sciences
Open Access status: hybrid
Estimated APC paid: $2,285
OpenAlex ID: W4401718205