%0 Journal Article
%@ 1081-6003
%A Roa, Javier
%A Pelaez Alvarez, Jesus
%D 2016
%F upm:52046
%J Advances in the Astronautical Sciences
%P 299-318
%T Introducing a degree of freedom in the family of generalized logarithmic spirals
%U http://oa.upm.es/52046/
%V 158
%X The versatility of the family of generalized logarithmic spirals is improved by introducing a degree of freedom in the solution. The low-thrust acceleration profile now includes a control term that affects both the magnitude and the direction of the thrust. Exact and fully analytic solutions to the trajectory, the velocity, the time of flight, etc. are made available. Two integrals of motion are preserved. The first one is a generalization of the equation of the energy and depends on the values of the control parameter. The second one relates to the equation of the angular momentum. The problem of finding spiral transfers between two arbitrary state vectors reduces to solving one algebraic equation with one unknown. The degree of freedom allows fixing the time of flight of the transfer. If the time of flight is fixed, then there are two equations with two unknowns. No other iterative procedures are required. Coast arcs can be introduced in the solution naturally. An explicit expression for the maximum acceleration reached along the transfer is provided. Thanks to the symmetry properties of the solution a simple algorithm for generating periodic orbits is presented. An arbitrary number of intermediate nodes can be introduced to improve the flexibility of the solution when facing optimization problems. An example of a low-thrust gravityassist Earth-Mars-Ceres trajectory shows that the solution is comparable to that obtained with other preliminary design techniques.
%Z DinĂ¡mica Espacial SDG-UPM