  We apply the analytical disturbing function for arbitrary inclination derived
in our previous work to characterize resonant width and libration of mean
motion resonances at arbitrary inclination obtained from direct numerical
simulations of the three-body problem. We examine the 2:1 and 3:1 inner Jupiter
and 1:2 and 1:3 outer Neptune resonances and their possible asymmetric
librations using a new analytical pendulum model of resonance that includes the
simultaneous libration of multiple arguments and their second harmonics. The
numerically-derived resonance separatrices are obtained using the Mean
Exponential Growth factor of Nearby Orbits (MEGNO chaos indicator). We find
that the analytical and numerical estimates are in agreement and that resonance
width is determined by the first few fundamental resonance modes that librate
simultaneously on the resonant timescale. Our results demonstrate that the new
pendulum model may be used to ascertain resonance width analytically, and more
generally, that the disturbing function for arbitrary inclination is a powerful
analytical tool that describes resonance dynamics of low as well as high
inclination asteroids in the solar system.
