Low-thrust trajectories are becoming increasingly important in the design of space
missions. The technological developments that allowed ion propulsion to become a competitive
option for missions such as Smart-1 and Deep Space 1 may be soon available
for many other advanced propulsion systems that promise to deliver long duration thrust
with high specic impulses and high reliability. Methods used to find the optimal trajectories
for spacecraft equipped with low-thrust capabilities, are based on direct and
indirect approaches highly dependent on the initial guess solution.
though successful in the detailed design of trajectories, fail in providing the designers
with a tool to effciently explore a large number of options at the early design phase. With this respect, the use
of analytical methods able to create solutions to the low-thrust problem could make a dierence. In his Ph.D. thesis Petropoulos
introduced for the first time a new analytical solution to the problem of low-thrust trajectories.
His solution, based on the use of an exponential sinusoid, is based on an inverse
dynamical calculation that leads to analytical expressions both for the thrusting history
and for the derivative of the polar anomaly, whenever tangential thrust is assumed. His
discovery added up to the small list of analytical solutions available for this increasingly
important problem. Moreover, his shape based method, inspired many other researchers.
The ACT started this project on the exponential sinusoids to find out their potentialities in a preliminary optimisation process. Along the way some amazing results have been obtained, suggesting that these shapes have actually "something" more than their pure geometrical interpretation. Together with the researchers at the University of Glasgow, the ACT deepened the understanding on this type of trajectory representation. In the 2nd edition of the Global Trajectory optimisation Competition (GTOC2), organized by JPL, the ACT used the exponential sinusoids to produce the final trajectory.