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There are analyzed two classical systems defined on twist-deformedacceleration-enlarged Newton-Hooke space-times - nonrelativistic particlemoving in constant field force $\vec{F}$ and harmonic oscillator model. It isdemonstrated that only in the case of canonical twist deformation the forceterms generated by space-time noncommutativity remain conservative for bothmodels.

Twisted acceleration-enlarged Newton-Hooke space-times and conservative force terms