scholarly journals A Numerical Study of Low-Thrust Limited Power Trajectories between Coplanar Circular Orbits in an Inverse-Square Force Field

2012 ◽  
Vol 2012 ◽  
pp. 1-24 ◽  
Author(s):  
Sandro da Silva Fernandes ◽  
Carlos Roberto Silveira Filho ◽  
Wander Almodovar Golfetto
Keyword(s):  
Force Field ◽  
Gradient Method ◽  
Trajectory Optimization ◽  
Optimization Problem ◽  
Numerical Study ◽  
Direct Method ◽  
Variation Theory ◽  
Second Variation ◽  
Low Thrust ◽  
Limited Power

A numerical study of optimal low-thrust limited power trajectories for simple transfer (no rendezvous) between circular coplanar orbits in an inverse-square force field is performed by two different classes of algorithms in optimization of trajectories. This study is carried out by means of a direct method based on gradient techniques and by an indirect method based on the second variation theory. The direct approach of the trajectory optimization problem combines the main positive characteristics of two well-known direct methods in optimization of trajectories: the steepest-descent (first-order gradient) method and a direct second variation (second-order gradient) method. On the other hand, the indirect approach of the trajectory optimization problem involves two different algorithms of the well-known neighboring extremals method. Several radius ratios and transfer durations are considered, and the fuel consumption is taken as the performance criterion. For small-amplitude transfers, the results are compared to the ones provided by a linear analytical theory.

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.

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.

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

Trajectory Optimization Applied to Space Rendezvous

2013 ◽  
Vol 756-759 ◽  
pp. 3466-3470
Author(s):  
Xu Min Song ◽  
Qi Lin
Keyword(s):  
Simulated Annealing ◽  
Optimization Model ◽  
Trajectory Optimization ◽  
Optimization Problem ◽  
Optimization Method ◽  
Nonlinear Constraints ◽  
Design Variables ◽  
Adaptive Simulated Annealing ◽  
Simulation Results

The trajcetory plan problem of spece reandezvous mission was studied in this paper using nolinear optimization method. The optimization model was built based on the Hills equations. And by analysis property of the design variables, a transform was put forward , which eliminated the equation and nonlinear constraints as well as decreaseing the problem dimensions. The optimization problem was solved using Adaptive Simulated Annealing (ASA) method, and the rendezvous trajectory was designed.The method was validated by simulation results.

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