We present here two examples of outputs of our algorithm: the former one (see Figure 4) is a Jupiter crossing asteroid with semimajor axis AU (a quite hard test for the algorithm); the computed solution is plotted with crosses indicating time steps, and the other lines are the level curves of the averaged Hamiltonian. Note that the solution fits quite well the level lines and the crosses show an increment in the velocity after the node crossing with Jupiter.

The second example (Figure 5) is an asteroid with the initial
conditions of the Apollo asteroid *1998 OH*; this seems to be an
easier case than the previous one, because the topology of the solution
does not change if we do not take into account the Earth and Mars; but
in computing the solution, we can see from the time dependence that there
is a difference in the velocity of the longitude of perihelion
if we take into account these planets: the proper frequency
is
arcsec/yr with the terrestrial planets included in the
model,
arcsec/yr without them. Such a difference could affect
significantly the location of the secular resonances.

2000-05-16