  In this paper, we identify criteria that guarantees the nonlinear orbital
stability of a given periodic traveling wave solution within the b-family
Camassa-Holm equation. These periodic waves exist as 3-parameter families (up
to spatial translations) of smooth traveling wave solutions, and their
stability criteria are expressed in terms of Jacobians of the conserved
quantities with respect to these parameters. The stability criteria utilizes a
general Hamiltonian structure which exists for every $b>1$, and hence applies
outside of the completely integrable cases ($b=2$ and $b=3$).
