  For a nonrelativistic classical particle undergoing arbitrary oscillations,
the generalized effective potential Y is derived from nonlinear
eigenfrequencies of the particle-field system. Specifically, the ponderomotive
potential is extended to a nonlinear oscillator, resulting in multiple branches
near the primary resonance. For a pair of natural frequencies in a beat
resonance, Y scales linearly with the internal actions and is analogous to the
dipole potential for a two-level quantum system. Thus cold quantum particles
and highly-excited quasiclassical objects permit uniform manipulation tools,
particularly, one-way walls.
