  In this paper we proposed a proposition: for any nonconservative classical
mechanical system and any initial condition, there exists a conservative one;
the two systems share one and only one common phase curve; the Hamiltonian of
the conservative system is the sum of the total energy of the nonconservative
system on the aforementioned phase curve and a constant depending on the
initial condition. Hence, this approach entails substituting an infinite number
of conservative systems for a dissipative mechanical system corresponding to
varied initial conditions. One key way we use to demonstrate these viewpoints
is that by the Newton-Laplace principle the nonconservative force can be
reasonably assumed to be equal to a function of a component of generalized
coordinates $q_i$ along a phase curve, such that a nonconservative mechanical
system can be reformulated as countless conservative systems. Utilizing the
proposition, one can apply the method of Hamiltonian mechanics or Lagrangian
mechanics to dissipative mechanical system. The advantage of this approach is
that there is no need to change the definition of canonical momentum and the
motion is identical to that of the original system.
