Zeki KASAP/ Elixir Adv. Math. 92 (2016) 38743-38748 38743 Introduction Dynamical systems are mathematical objects used to model physical phenomena whose state changes over time that its can be viewed in two different ways: the internal and the external view. The prototype (mechanical) problem is describing the motion of the planets. It is natural to give a complete characterization of the motion of all planets that this involves careful analysis of the effects of gravitational pull and the relative positions of the planets in a system for mechanical problems. Classical mechanics, under the influence of specified force laws, is the investigation of the motion of dynamical systems of particles in Euclidean three-dimensional space. Also, the motion's evolution determined by Newton's second law that is a differential equation. So, mechanical problems are to determine the positions of all the particles at all times for given certain laws determining physical forces, some boundary conditions on the positions of the particles at some particular times. Classical mechanics of a system of point particles and rigid object is usually divided into statics, kinematics and dynamics. Classical field theory utilizes traditionally the language of Hamiltonian dynamics. Hamiltonian mechanics is a theory developed as a reformulation of classical mechanics. Also, this theory has extended to time-dependent classical mechanics. Contact geometry has been seen to underlay many physical phenomena and be related to many other mathematical structures. Contact geometry is in many ways an odd- dimensional counterpart of symplectic geometry such that it belongs to the even-dimensional world. Both contact and symplectic geometry are motivated by the mathematical formalism of classical and analytical mechanics. Besides, one can consider either the even-dimensional phase space of a mechanical system or the odd-dimensional extended phase space that includes the time variable. A mathematical model is a precise representation of a system's dynamics used to answer questions via analysis and simulation. The mathematical models choose depends on lots of questions, so there may be multiple models for physical systems in the space. In this study, the movements for moving objects modeling Hamilton equations to be found on the space defined on contact 5-manifolds. Also, the graphics of the path taken by the object that will be drawn when the angle changes. Bellettini obtained almost complex structures J that satisfy, for any vector v in the horizontal distribution, dα(v,Jv)=0 such that a contact manifold is (M΁,α) [1]. Janssens and Vanhecke determined an orthogonal decomposition of the vector space of some curvature tensors on a co-Hermitian real vector space [2]. Chaubey studied some geometrical properties of almost contact metric manifolds equipped with semi-symmetric non- metric connection [3]. Kodama classified the local structure of complex contact manifolds of dimension three with Legendrian vector fields [4]. Piercey defined contact manifolds and identify simple examples and basic properties [5]. Doubrov and Komrakov submitted the complete classification of all real Lie algebras of contact vector fields on the first jet space of one-dimensional submanifolds in the plane [6]. Attarchi and Rezaii submitted that a comprehensive study of contact and Sasakian structures on the indicatrix bundle of Finslerian warped product manifolds is reconstructed [7]. Kashiwara showed that the existence of the stack of micro-differential modules on an arbitrary contact manifold, although he cannot expect the global existence of the ring of micro-differential operators [8]. Manev and Gribachev examined the main classes of almost contact manifolds with B-metric [9]. Iglesias-Ponte and Wade gave simple characterizations of contact 1-forms in terms of E-mail address: zekikasap@hotmail.com © 2016 Elixir All rights reserved ARTICLE INFO Article history: Received: 18 January 2016; Received in revised form: 1 March 2016; Accepted: 4 March 2016; Keywords Contact Manifold, Mechanical System, Dynamic Equation, Hamiltonian Formalism. Hamilton Equations on a Contact 5-Manifolds Zeki KASAP ABSTRACT It is well known that a dynamical system is a concept in mathematics where a fixed rule describes how a point in a geometrical space depends on time. A mathematical model is a precise representation of a system's dynamics used to answer questions via analysis and simulation. Mathematica models allow us to reason about a system and make predictions about who a system will behave. Contact geometry is the odd-dimensional analogue of symplectic geometry. It is close to symplectic geometry and like the latter it originated in questions of classical and analytical mechanics. If contact geometry is considered as a symplectic geometry, it has broad applications in mathematical physics, geometrical optics, classical mechanics, analytical mechanics, mechanical systems, thermodynamics, geometric quantization and applied mathematics such as control theory. It is well known fact that one way of solving problems in classical mechanics occur with the help of the Hamilton equations. Hamiltonian method is particularly important because of its utility in formulating quantum mechanics. In this study, Hamilton equations as representive the object motion were found on a contact 5-manifolds. Also, implicit solutions of the differential equations found in this study are solved by Maple computation program. © 2016 Elixir All rights reserved. Elixir Adv. Math. 92 (2016) 38743-38748 Advanced Mathematics Available online at www.elixirpublishers.com (Elixir International Journal)