Weyl-Euler-Lagrange equations on twistor space for tangent structure

Abstract

Twistor spaces are certain complex three-manifolds, which are associated with special conformal Riemannian geometries on four-manifolds. Also, classical mechanic is one of the major subfields for mechanics of dynamical system. A dynamical system has a state determined by a collection of real numbers, or more generally by a set of points in an appropriate state space for classical mechanic. Euler-Lagrange equations are an efficient use of classical mechanics to solve problems using mathematical modeling. On the other hand, Weyl submitted a metric with a conformal transformation for unified theory of classical mechanic. This paper aims to introduce Euler-Lagrage partial differential equations (mathematical modeling, the equations of motion according to the time) for the movement of objects on twistor space and also to offer a general solution of differential equation system using the Maple software. Additionally, the implicit solution of the equation will be obtained as a result of a special selection of graphics to be drawn. © 2016 World Scientific Publishing Company.