Physical interpretation of invariance of vector differential Operators in Three Orthogonal Coordinate Systems and a Case Study of wall and globe of death

Abstract

In the present study, effect of operators on fundamental physical quantities in three orthogonal coordinate systems was analyzed using differential equations. The mathematical expression for position vector and its magnitude, velocity and 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 vector were derived and their physical significance was illustrated. Similarly, the operation of Laplacian operator on magnitude of position vector was also studied. The study highlighted the invariance in results of all operations in three orthogonal coordinates systems. An investigation has been performed to describe wall of death and globe of death problem in appropriate orthogonal coordinate systems. The interpretations in term of velocity, acceleration, and net force acting on vehicle are explained in details.