Noncommuting contractions of oscillators with constant force

We find two noncommuting contractions of the Lie algebras and , realized as the symmetry algebras of N-dimensional isotropic harmonic and repulsive oscillators of spring constant k ∈ ℜ, with a constant force of magnitude f. The contraction limit to the symmetry algebra of the N-dimensional free system is (k, f) → (0, 0). We take two paths in this plane, determined by the order of contraction of the two parameters, and show that they yield two closely related - but distinct - Euclidean-type symmetry algebras for the common contracted system. We also show briefly how the wavefunctions of the one-dimensional harmonic oscillator reduce to plane waves along the above two paths.