Abstract
We use a simplified averaged Hamiltonian to study the restricted elliptic planar three-body problem near first-order resonance. The Hamiltonian is truncated in first order in the eccentricities of the asteroid and Jupiter. The model includes the action of the eccentricity of Jupiter in first order that factored the critical argument associated with the perihelion of Jupiter's orbit. Long-period terms in both eccentricities are neglected. This simplified model lets us easily interpret the types of motion of the asteroid. The model gives a qualitative description of the motion of first-order resonant asteroids, although it seems unable to reproduce the quantitative results obtained by Schubart for the Hilda group.
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