On the lagrangian and hamiltonian mechanical in 3-dimensional minkowski space structers

This thesis consists of four chapters. In the first chapter, a brief historical background of the Minkowski space-time concept is presented, followed by a detailed examination of its fundamental geometric and physical properties. Subsequently, the jet bundle structure to be used in the study is introduced, and its mathematical foundations are established. Additionally, all geometric concepts and structures necessary for understanding the jet bundle are systematically addressed. In the second chapter, Lagrangian mechanical systems are constructed on the Minkowski jet bundle structure defined in the first chapter, and the corresponding differential equations are solved to derive the associated Lagrangian energy equations. In the third chapter, Hamiltonian mechanical systems are developed based on the same structure, and by solving the resulting differential equations, the Hamiltonian energy equations are obtained. In the final chapter, the Lagrangian energy equation is rederived using kinetic and potential energy expressions, and the mathematical reasons why the Hamiltonian energy equations cannot be directly derived from this structure are explained. Finally, an example application is provided to enhance the understanding of the theoretical framework.