  In this paper, we study the stability of smooth solitary waves for the
$b$-family of Camassa-Holm equations. We verify the stability criterion
analytically for the general case $b>1$ by the idea of the monotonicity of the
period function for planar Hamiltonian systems and show that the smooth
solitary waves are orbitally stable, which gives a positive answer to the open
problem proposed by Lafortune and Pelinovsky [S. Lafortune, D. E. Pelinovsky,
Stability of smooth solitary waves in the $b$-Camassa-Holm equation].
