author = "Formiga, Jorge Kennety da Silva and Santos, Denilson Paulo Souza 
          affiliation = "{Faculdade de Tecnologia (FATEC)} and {Instituto Nacional de 
                         Pesquisas Espaciais (INPE)}",
                title = "An analytical description of the three-dimensional swing-by",
              journal = "Computational and Applied Mathematics",
                 year = "2015",
               volume = "34",
               number = "2",
                pages = "491--506",
                month = "July",
             keywords = "Gravity assist, Orbital maneuver, Swing-by.",
             abstract = "This paper presents an analytical description of the 
                         three-dimensional swing-by. The main goal is to derive analytical 
                         equations for the variations of all the orbital elements of a 
                         particle that makes a close approach with a celestial body. Those 
                         derivations are based in the {"}patched-conics{"} approximation, 
                         which means that a series of keplerian orbits are assumed for the 
                         particle. After deriving the equations they are verified using the 
                         Tisserand's Criterion, which is a rule that must be followed by 
                         the keplerian elements before and after a swing-by. Then, 
                         simulations using those equations are made to verify the effects 
                         of the swing-bys. The final contribution is a complete set of 
                         analytical equations, developed and confirmed by numerical 
                  doi = "10.1007/s40314-014-0139-6",
                  url = "http://dx.doi.org/10.1007/s40314-014-0139-6",
                 issn = "2238-3603",
             language = "en",
        urlaccessdate = "18 jan. 2021"