Lagrange and Hamilton formalisms derived from variational calculus can be applied nearly in all engineering sciences. In this study, the reader is introduced using tensorial variables in covariant and contravariant forms, to the extended Lagrangian and herewith to the modified momentum . Through both, the extended Hamiltonian of a dissipative engineering system is derived to analyze the engineering system in an analytical way. In addition, a nonconservative Hamiltonian H (aun) for systems with elements of higher order is introduced in a similar manner. Moreover, different forms of extended Hamiltonian are represented. How these forms are achieved and how to derive the equations of generalized motion in different forms is also explained. As an example, a coupled electromechanical system in different formulations is given on behalf of the reader. The example is even extended to a case including some elements of higher order.