The Hamiltonian Formalism for Dissipative Mechanical Systems

In this paper show that dissipative mechanical systems can be represented as Hamiltonian formalism. We have defined an expanded Hamiltonian function that leads to a unique conservative system for every phase flow of a dissipative mechanical system. We have demonstrated, whether the class of dissipative mechanical system has an analytical solution or not, it can be represented as an infinite number of Hamilton’s equations corresponding to varied initial conditions, in other words every phase flow curve of a dissipative systems can be consider as a phase flow curve of a distinguished conservative system. With a common initial condition the dissipative system and the conservative system have a exactly same solution. The major trick is that by the Newton-Laplace principle the nonconservative force can be reasonably assumed as a function of a component of generalized coordinates qi along, so that dissipative mechanical system can be converted into a group of conservative mechanical systems with Hamiltonian which is total energy of the original dissipative system. We can investigate a group of conservative systems instead of an original dissipative mechanical system.