Volume no :15, Issue no: 1, February (2016)

EULER-LAGRANGE EQUATIONS WITH 3-DIMENSIONAL REAL NUMBER SPACE ON AN ALMOST PARACONTACT MANIFOLD

Author's: Zeki Kasap
Pages: [61] - [79]
Received Date: December 26, 2015; Revised February 17, 2016
Submitted by:
DOI: http://dx.doi.org/10.18642/jpamaa_7100121610

Abstract

We consider Euler-Lagrange equations on almost paracontact manifolds. It is well known that the geometry of almost contact manifolds is a natural extension in the odd dimensional case of almost Hermitian geometry. A Hermitian manifold is a complex manifold with a Hermitian metric on its holomorphic tangent space. Also, the contact geometry as symplectic geometry has large and comprehensive applications in physics, geometrical optics, classical mechanics, thermodynamics, geometric quantization, and applied mathematics. On the other hand, one way of solving problems in classical and analytical mechanics is through use of the Euler-Lagrange equations. The purpose of the present paper is to solve the problems of classical mechanics with 3-dimensional real number space on an almost paracontact manifold by using Euler-Lagrange equations.

Keywords

symplectic manifold, contact manifold, mechanical system, dynamic equation, Lagrangian formalism.