  In this paper, we present an explicit form in terms of end-point data for the
classical action $S_{2n}$ evaluated on extremals satisfying the Hamilton-Jacobi
equation for each member of a hierarchy of classical non-relativistic
oscillators characterized by even power potentials (i.e., attractive potentials
$V_{2n}(y_{2n})={\frac{1}{2n}}k_{2n}y_{2n}^{2n}(t)|_{n{\geq}1}$). The nonlinear
quartic oscillator corresponds to $n=2$ while the harmonic oscillator
corresponds to $n=1$.
