A Physical Space-modeled Approach to Lagrangian Equations with Bundle Structure for Minkowski 4-space

Abstract

The aim of this paper is to apply the necessary and sufficient conditions of well-known Lagrangian equations with time dependent case for Minkowski 4-space. Many fundamental geometrical properties for time dependent Minkowski 4-space have been obtained in this paper. The energy equations have been applied to the numerical example in order to test its performance. In the numerical examples, we have studied with two time parameters (earth and space time) for accordance to Minkowski 4-space coordinates. This idea is an interesting approach to energy function with Earth-time and Space-time in physical comment. Moreover, velocity and two time dimensions for energy movement equations have been presented a new concept. This study show some physical application of those equations and interpretations are made in Minkowski space too. Results showed that Lagrangian functions for any surface are same type and depend on time coordinates.