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.