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Optimization of electric propulsion trajectory using the oneparameter continuation is considered. The optimal control problem is reduced into boundary value problem by means of maximum principle. The oneparameter continuation essence is immersion the boundary value problem into the oneparametric family of boundary value problems. Differentiating the residuals of boundary value problem with respect to continuation parameter reduces this problem into the initial value problem.
Usage the oneparameter continuation method for dynamical system, which is represented by ordinary differential equations, results in the nested integration of differential equations. The dynamical system integration produces boundary residuals, and this residuals are used to form right parts of differential equations of oneparameter continuation method. This method realization requires rather high computational productivity. As a result an effective usage of this method became feasible in the last decade only.
The review of oneparameter continuation versions and trajectory optimization results are presented, including:
 planetary solar and nuclear electric propulsion mission optimization (both rendezvous and flyby) for variable specific impulse problem;
 lowthrust trajectory optimization (variable specific impulse problem) within the frame of restricted problem of three bodies, including transfers to the libration points and mission to the Moon;
 minimum time lowthrust transfer between noncoplanar elliptical orbits (constant specific impulse problem) including insertion into GEO from elliptical transfer orbit.
The first version of oneparameter continuation method for planetary mission optimization was realized by author in the 1994. The 6years method exploitation demonstrates its extremely effectiveness (much better then conventional direct and indirect optimization methods) and practical regularity for such kind of optimization problems. In particularity, there were found optimal lowthrust trajectories to Mercury which includes up to 50 complete orbits around the Sun (nonaveraged ones), optimal rendezvous and flyby of planets and small bodies in the range from Mercury to Pluto. The bifurcation of optimal lowthrust trajectories was analyzed, the lowthrust trajectories using gravity assist maneuvers were optimized.
The features of oneparametric continuation versions for lowthrust trajectory optimization are discussed. The Windows application EPOCH for lowthrust heliocentric trajectory optimization is demonstrated.
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