We consider the modified Emden equation (MEE) for position-dependent mass (PDM) classical particles. We use the most general solution for the simple harmonic oscillator’s linear dynamical equation (i.e., the initial conditions shall be identified by the PDM-MEE problem at hand) and report the most general solution for the MEE. We map MEE-solution, using a nonlocal point transformation, into the effectively PDM-MEE. Two PDM-MEE-type classical particles are used as illustrative examples, and their exact solutions are reported. Under specific parametric considerations, the phase-space trajectories are reported for the MEE-type and for PDM-MEE-type classical particles.
PACS numbers: 05.45.-a, 03.50.Kk, 03.65.-w