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

A Sort of Relation among a Dissipative Mechanical System and Conservative Ones