  In this study, a new expansion of planetary disturbing function is developed
for describing the resonant dynamics of minor bodies with arbitrary
inclinations and semimajor axis ratios. In practice, the disturbing function is
expanded around circular orbits in the first step and then, in the second step,
the resulting mutual interaction between circular orbits is expanded around a
reference point. As usual, the resulting expansion is presented in the Fourier
series form, where the force amplitudes are dependent on the semimajor axis,
eccentricity and inclination and the harmonic arguments are linear combinations
of the mean longitude, longitude of pericenter and longitude of ascending node
of each mass. The resulting new expansion is valid for arbitrary inclinations
and semimajor axis ratios. In the case of mean motion resonant configuration,
the disturbing function can be easily averaged to produce the analytical
expansion of resonant disturbing function. Based on the analytical expansion,
the Hamiltonian model of mean motion resonances is formulated, and the
resulting analytical developments are applied to Jupiter's inner and co-orbital
resonances and Neptune's exterior resonances. Analytical expansion is validated
by comparing the analytical results with the associated numerical outcomes.
