Dynamics Equations with Almost Complex Structures on Contact 5-Manifolds

Abstract

Contact geometry is the odd-dimensional analogue of symplectic geometry with certain manifolds of odd dimension. It is close to symplectic geometry and like the latter it originated in questions of classical and analytical mechanics. Contact geometry has, as does symplectic geometry, broad applications in mathematical physics, geometrical optics, classical mechanics, analytical mechanics, mechanical systems, thermodynamics, geometric quantization and applied mathematics such as control theory. On the other hand, one way of solving problems in classical mechanics is with the help of the Euler-Lagrange and the Hamilton equations. In this study, Euler-Lagrange mechanical equations as representing the motion of the body were found on contact 5-manifolds. Also, closed solutions of the differential equations found in this study are solved by symbolic computation program.