The synthesis of gravity assist maneuvers sequence of the spacecraft to achieve high inclined orbits over ecliptic

In the connection with the preparation and conduct of lot of space missions, providing an increase of inclination of the orbit over ecliptic with the use of low-cost gravitational maneuvers (GAM) near the planets and their moons, also small bodies of the Solar system, NASA’s, ESA’s, JAXA’s teams also domestic experts actively analyzes the spatial (3D) implementations of such maneuvers. The corresponding calculations to create the actual ballistic space mission design to explore the inner heliosphere out of ecliptic areas (Russian mission “Interheliozond”, ESA’s mission «Solar Orbiter») demanded. This paper is focused on the development of synthesis of chains of 3D multibody GAM's algorithms which implementation leads to a significant increase in the spacecraft's orbit above the plane of the ecliptic. Simultaneously for earlier obtained analytical formulas by the authors [1] generalization for inclination changes with the using of gravity assists on the case of elliptic orbits of planets and the spacecraft accomplished.