  We derive the precise stability criterion for smooth solitary waves in the
b-family of Camassa-Holm equations. The smooth solitary waves exist on the
constant background. In the integrable cases b = 2 and b = 3, we show
analytically that the stability criterion is satisfied and smooth solitary
waves are orbitally stable with respect to perturbations in $H^3(\mathbb{R})$.
In the non-integrable cases, we show numerically and asymptotically that the
stability criterion is satisfied for every b > 1. The orbital stability theory
relies on a different Hamiltonian formulation compared to the Hamiltonian
formulations available in the integrable cases.
