  An equation is obtained to find the Lagrangian for a one-dimensional
autonomous system. The continuity of the first derivative of its constant of
motion is assumed. This equation is solved for a generic nonconservative
autonomous system that has certain quasi-relativistic properties. A new method
based on a Taylor series expansion is used to obtain the associated Hamiltonian
for this system. These results have the usual expression for a conservative
system when the dissipation parameter goes to zero. An example of this approach
is given.
