  We phenomenologically analyze short DNA rings' stability by discussing the
second variation of its elastic free energy. Through expanding the perturbation
functions as Fourier series, we obtain DNA rings' stability condition in a
general case. By reviewing the relationship between the Kirchhoff model and the
worm-like road chain (WLRC) model, we insert a spontaneous curvature term which
can partly reflect the twist angle's contribution to free energy in the WLRC
model and name this extended model the EWLRC model. By choosing suitable
spontaneous curvature, stability analysis in this model provide us with some
useful results which are consistent with the experimental observations.
