  Two dynamical systems with same symmetry should have features in common, and
as far as their shared symmetry is concerned, one may represent the other. The
three light quark constituents of the hadrons, a) have an approximate flavor
SU(3) symmetry, b) have an exact color SU(3) symmetry, and c) as spin 1/2
particles, have a Lorentz SO(3,1) symmetry. So does a 3D harmonic oscillator.
a) Its Hamiltonian has the SU(3) symmetry, breakable if the 3 fundamental modes
of oscillation are not identical. b) The 3 directions of oscillation have the
permutation symmetry. This enables one to create three copies of unbreakable
SU(3) symmetry for each mode of the oscillation, and mimic the color of the
elementary particles. And c) The Lagrangian of the 3D oscillator has the
SO(3,1) symmetry. This can be employed to accommodate the spin of the
particles. In this paper we draw up a one-to-one correspondence between the
eigen modes of the Poisson bracket operator of the 3D oscillator and the flavor
multiplets of the particles, and between the permuted modes of the oscillator
and the color and anticolor multiplets of the particles. Gluons are represented
by the generators of the color SU(3) symmetry of the oscillator. Harmonic
oscillators are common place objects and, wherever encountered, are
analytically solvable. Elementary particles, on the other hand, are abstract
entities far from one's reach. Understanding of one may help a better
appreciation of the other.
