We perform an accurate modelling of orbital evolution of dust grains t
aking into account both the ejection parameters derived from the analy
sis of the dust tail of each considered parent comet (Fulle 1989), and
the integration of the Newton equations in the context of a nine-body
problem (Sun, seven major planets and the dust particle) plus solar r
adiation and wind forces. Among Short Period Comets (SPC) we have sele
cted P/Schwassmann-Wachmann 1 (P/SW1) and P/Griegg-Skjellerup (P/GS),
which represent two significantly different objects from a dynamical p
oint of view. Dust from P/SW1 is dominated by Jupiter perturbations: a
fter 2 10(4) years, about 7% of the grains are ejected in hyperbolic o
rbits, 80% of the grains have the perihelion out of 4 AU from the Sun,
and only 1% of them reaches the Sun distance of 1 AU, thus contributi
ng to the inner zodiacal cloud. Dust from P/GS is dominated by the P-R
drag, although large,grains, due to their longer collapse lifetime, a
re sensitive to Jupiter perturbations. Therefore the Tisserand criteri
on represents a useful tool both to estimate the orbital evolution of,
grains larger than 100 mu m (i.e. the most likely canditates to replen
ish the zodiacal dust cloud, Grun et al. 1985). and in distinguishing
the parent sources of meteoroids collected with near Earth space exper
iments able to measure the impact velocity vectors. Jupiter perturbati
ons oppose to the P-R drag forces and reduce significantly the contrib
ution of SPC to the inner zodiacal dust: the simple sum of the dust ma
ss contribution from each SPC may be an overestimate of their actual s
upply.