Representation of Hamiltonian Formalism in Dissipative Mechanical System

Hamiltonian mechanics is the root of classical mechanics. Hamiltonian function is the modified version of Lagrangian function which is of the first order differential equations with generalized coordinates, generalized momentum and time. So, Hamiltonian formulations play an important role in classical mechanics as well as in mechanical systems. In this study, we have established Hamiltonian formalism for dissipative system. We have demonstrated that, whether the class of dissipative mechanical system has an analytical solution or not, it can be represented as a Hamiltonian formalism. Dissipative system deals with the Damping force, Mechanical energy, Principle of least action, First integral, Jacobian matrix and the Non-conservative system deals with Fractional derivatives, Hamiltonian systems, non-conservative systems and Laplace transform.