Hamiltonian mechanical system with split quaternions

Abstract

In this article, firstly we study about geometrical applications of split quaternions. Then, we obtain Hamitonian mechanical systems with Split quaternions. Quaternionic and Coquaternionic (split analoque of quaternions) extensions of Hamiltonian mechanics are introduced and are shown as offer a unifying framework for quantum mechanics. This study leads to the possibility of employing algebraic techniques of quaternions and coquaternions to absorbing in quantum mechanics. The founded equations are compared with the Hamiltonian energy equations generally are known and the Hamilton energy equations are obtained in Minkowski space. Keywords Hamiltonian Mechanical System, Minkowski Space, Jet bundles, Hamiltonian Energy Equations, Quaternion, Split Quaternion