loading page

Physical interpretation of invariance of vector differential Operators in Three Orthogonal Coordinate Systems and a Case Study of wall and globe of death
  • +4
  • Dipak Gapale,
  • Sandeep Arote,
  • Prashant Baviskar,
  • Sainath Navale,
  • Balasaheb Palve,
  • Abbas Pathan,
  • Sanjaykumar Dalvi
Dipak Gapale
Sangamner College

Corresponding Author:[email protected]

Author Profile
Sandeep Arote
Sangamner College
Author Profile
Prashant Baviskar
Sangamner College
Author Profile
Sainath Navale
Sangamner College
Author Profile
Balasaheb Palve
Sangamner College
Author Profile
Abbas Pathan
Sangamner College
Author Profile
Sanjaykumar Dalvi
Sangamner College
Author Profile

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.