Lagrangian Dynamical Systems with Three Para-complex Structures

Ibrahim Yousif Ibrahim Abad Alrhman

doi:10.11648/j.ijssam.20190404.11

Abstract

This paper aims to present Lagrangian Dynamical systems formalism for mechanical systems using Three Para- Complex Structures, which represent an interesting multidisciplinary field of research. As a result of this study, partial differential equations will be obtained for movement of objects in space and solutions of these equations. In this study, some geometrical, relativistic, mechanical, and physical results related to Three Para- Complex Structures mechanical systems broad applications in mathematical physics, geometrical optics, classical mechanics, analytical mechanics, mechanical systems, thermodynamics, geometric quantization and applied mathematics such as control theory.

Highlights

The geometric study of dynamical systems is an important chapter of contemporary mathematics due to its applications in Mechanics, Theoretical Physics
We study dynamical systems with Three Almost para Complex Structures
Α: I ⊂ R → T∗M = b is an integral curve of the Lagrangian vector field Xd, i. e., dα(t

Summary

Introduction

The geometric study of dynamical systems is an important chapter of contemporary mathematics due to its applications in Mechanics, Theoretical Physics. If M is a differentiable manifold that corresponds to the configuration space, a dynamical system can be locally given by a system of ordinary differential equations of the form. A dynamical system is givenby a vector field X on the manifold whose integral curves, aregiven by the equations of evolution,. Kahlerian manifold and the geometric results on a paracomplex mechanical systems were found [2]. The geometrical, relativistical, mechanical and physical results related to para/. Pseudo-Kahler mechanical systems were given, too [3]. We study dynamical systems with Three Almost para Complex Structures.

Preliminaries

Lagrangian Dynamical Systems

Conclusions