Optimum low-thrust limited power transfers between neighbouring elliptic non-equatorial orbits in a non-central gravity field

1995 ◽  
Vol 35 (12) ◽  
pp. 763-770 ◽  
Author(s):  
Sandro Da Silva Fernandes
Keyword(s):  
Gravity Field ◽  
Low Thrust ◽  
Limited Power

scholarly journals Optimization of Low-Thrust Limited-Power Trajectories in a Noncentral Gravity Field—Transfers between Orbits with Small Eccentricities

2009 ◽  
Vol 2009 ◽  
pp. 1-35 ◽  
Author(s):  
Sandro da Silva Fernandes
Keyword(s):  
Gravity Field ◽  
Perturbation Technique ◽  
Canonical System ◽  
State Variables ◽  
Low Thrust ◽  
Lie Series ◽  
Zonal Harmonic ◽  
First Order ◽  
Mayer Problem ◽  
Limited Power

Numerical and first-order analytical results are presented for optimal low-thrust limited-power trajectories in a gravity field that includes the second zonal harmonicJ2in the gravitational potential. Only transfers between orbits with small eccentricities are considered. The optimization problem is formulated as a Mayer problem of optimal control with Cartesian elements—position and velocity vectors—as state variables. After applying the Pontryagin Maximum Principle, successive canonical transformations are performed and a suitable set of orbital elements is introduced. Hori method—a perturbation technique based on Lie series—is applied in solving the canonical system of differential equations that governs the optimal trajectories. First-order analytical solutions are presented for transfers between close orbits, and a numerical solution is obtained for transfers between arbitrary orbits by solving the two-point boundary value problem described by averaged maximum Hamiltonian, expressed in nonsingular elements, through a shooting method. A comparison between analytical and numerical results is presented for some maneuvers.

scholarly journals Optimization of sprint interplanetary trajectories with nuclear bimodal thermal propulsion

2019 ◽  
pp. 74-77
Author(s):  
O. M. Kharytonov ◽  
S. R. Savchenko ◽  
N. Miranda
Keyword(s):  
Optimization Problem ◽  
Electrical Power ◽  
Propulsion System ◽  
Low Thrust ◽  
Small Times ◽  
Limited Power ◽  
Trajectory Method ◽  
Payload Mass ◽  
Interplanetary Missions ◽  
High Thrust

Interplanetary missions require fast and fuel-efficient transfers. Combining small times transfers of high-thrust and efficiency of low-thrust propulsion can provide a good compromise. Saving an amount of fuel from the initial high-thrust burn and using it to correct the trajectory could lead to an economy of fuel. We investigated the optimal way to take advantages of both high and low-thrust propulsion benefits in order to maximize the payload mass of the mission. Using a simple model of ideal engine of limited power and the transporting trajectory method, we determined the analytical expression of final payload mass. The solution of the optimization problem gave us the optimal repartition of fuel between high and low-thrust maneuvers for a given thrust of thermal propulsion and electrical power of low-thrust propulsion system. As the mass of the low-thrust propulsion system depends on the electrical power, we took it into account to determine the optimal electrical power for a sprint trajectory in a given time. As a result, we could obtain the interval of transfer time for which the combination of high and low thrust becomes optimal.

Optimal low-thrust, limited power transfers between arbitrary elliptical orbits

1977 ◽  
Vol 4 (5-6) ◽  
pp. 511-540 ◽  
Author(s):  
Jean-Pierre Marec ◽  
Nguyen X. Vinh
Keyword(s):  
Low Thrust ◽  
Limited Power ◽  
Elliptical Orbits

scholarly journals Numerical and Analytical Study of Optimal Low-Thrust Limited-Power Transfers between Close Circular Coplanar Orbits

2007 ◽  
Vol 2007 ◽  
pp. 1-23 ◽  
Author(s):  
Sandro da Silva Fernandes ◽  
Wander Almodovar Golfetto
Keyword(s):  
Boundary Value Problem ◽  
Optimization Problem ◽  
Analytical Study ◽  
Numerical Study ◽  
Boundary Value ◽  
Performance Criterion ◽  
Point Boundary ◽  
Low Thrust ◽  
Transformation Theory ◽  
Limited Power

A numerical and analytical study of optimal low-thrust limited-power trajectories for simple transfer (no rendezvous) between close circular coplanar orbits in an inverse-square force field is presented. The numerical study is carried out by means of an indirect approach of the optimization problem in which the two-point boundary value problem, obtained from the set of necessary conditions describing the optimal solutions, is solved through a neighboring extremal algorithm based on the solution of the linearized two-point boundary value problem through Riccati transformation. The analytical study is provided by a linear theory which is expressed in terms of nonsingular elements and is determined through the canonical transformation theory. The fuel consumption is taken as the performance criterion and the analysis is carried out considering various radius ratios and transfer durations. The results are compared to the ones provided by a numerical method based on gradient techniques.

A numerical study for optimal low-thrust limited power transfers between coplanar orbits with small eccentricities

2016 ◽  
Vol 35 (3) ◽  
pp. 907-936
Author(s):  
Francisco das Chagas Carvalho ◽  
Sandro da Silva Fernandes ◽  
Rodolpho Vilhena de Moraes
Keyword(s):  
Numerical Study ◽  
Low Thrust ◽  
Limited Power
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