The Experts below are selected from a list of 39 Experts worldwide ranked by ideXlab platform

Dilmurat M. Azimov - One of the best experts on this subject based on the ideXlab platform.

  • Extremal Control and Guidance Solutions for Orbital Transfer with Intermediate Thrust
    The Journal of the Astronautical Sciences, 2015
    Co-Authors: Dilmurat M. Azimov, Fernando A. Sanabria
    Abstract:

    Mayer’s variational problem of determining optimal trajectories of motion with Constant Exhaust Velocity and limited mass-flow rate in a Newtonian field is considered. Analytical solutions for extremal transfers between two coplanar elliptical orbits via one and two intermediate-thrust arcs are presented. It is shown that in the cases of transfers via one and two intermediate-thrust arcs, the orbital parameters have to satisfy respectively two constraints and one constraint imposed by the continuity conditions formed at the junctions. This means that respectively two and one of these orbital parameters must not be arbitrary. Furthermore, by utilizing the analytical solutions for the intermediate-thrust arcs, the corresponding extremal guidance laws for a transfer between two points with arbitrary position vectors and for a transfer between elliptical orbits are presented. The guidance commands are formulated in terms of commanded thrust angle and commanded mass-flow rate. A numerical example illustrating the proposed trajectory and guidance solutions is discussed. The results of the computations are compared to those of similar one- and two- impulsive transfers, and a low-thrust orbit raising maneuver. It is demonstrated that for some eccentricities of the terminal orbits, the fuel consumption for a transfer via an intermediate-thrust arc is comparable to that of the two-impulsive transfers. Analyses show that a maneuver with such an arc may be fuel-efficient with longer duration and higher thrust than that of the low-thrust maneuver. The trajectory computations and guidance performances are illustrated by graphical relationships.

  • Extremal Analytical Solutions for Intermediate-Thrust Arcs in a Newtonian Field
    Journal of Guidance Control and Dynamics, 2010
    Co-Authors: Dilmurat M. Azimov
    Abstract:

    The variational problem of determining optimal trajectories of motion with Constant Exhaust Velocity and limited mass-flow rate in a central Newtonian field is considered. The first-order necessary conditions of optimality reduce the problem to a Hamiltonian canonical system of equations for intermediate- and maximum-thrust arcs, both of which have no complete analytical solutions to date. The approach used in this work is based on the analytical integration of the canonical system by employing its first integrals and invariant expressions. Several new classes of extremal analytical solutions for planar intermediate-thrust arcs with free and fixed flight times are presented. The solutions describe families of spiral trajectories around the center of attraction. The main result of the paper is that, in their current form with known integrals, the differential equations of the variational problem for intermediate-thrust arcs are integrable in elementary functions and quadratures, and the solution of this problem with such arcs can be reduced to a system of algebraic continuity equations formed for each junction point. These solutions can be used as representative reference trajectories for guidance algorithms and to compute initial values of Lagrange multipliers for high-fidelity trajectory optimization software. As an illustrative example, the transfer maneuver to a given elliptical parking orbit using an intermediate-thrust arc is discussed. Results of simulations for three study cases containing the change of eccentricity and semiparameter of the parking orbit and specific impulses are presented.

  • Extremal Rocket Motion with Maximum Thrust in a Linear Central Field
    Journal of Spacecraft and Rockets, 2001
    Co-Authors: Dilmurat M. Azimov, Robert H. Bishop
    Abstract:

    TheMayer variationalproblem of determining optimal trajectories of a rocket movingwith maximumthrust in a thin spherical layer within a central Newtonian Ž eld is considered. The present work is devoted to the analytical investigation of maximum thrust arcs for a rocket engine with Constant Exhaust Velocity and limited mass  ow rate using the necessary conditions of optimality.Many problems of practical interest admit an approximation of the central Newtonian Ž eld by a linear central Ž eld. It is shown that the linear central Ž eld assumption is valid when the thrust vector is nearly tangential to the orbit and the rocket remains in a sufŽ ciently thin spherical layer during the maneuver. When the linear central Ž eld approximationis utilized, analytic closed-form expressions are obtained describing optimal maximum thrust space trajectories. The problem of optimal orbit transfer between coplanar circular orbits is considered to illustrate the solution process, which comprises two maximumthrust and three null thrust arcs. It is shown that solutionsof the problem are comparablewith solutionsbased on assumptions of instantaneous changes in Velocity, including the Hohmann transfer.

  • ANALYTIC SOLUTIONS FOR INTERMEDIATE-THRUST ARCS OF ROCKET TRAJECTORIES IN A NEWTONIAN FIELD
    Journal of Applied Mathematics and Mechanics, 1996
    Co-Authors: Dilmurat M. Azimov
    Abstract:

    Abstract Mayer's variational problem of determining the optimum trajectories of a rocket moving with Constant Exhaust Velocity and bounded mass flow rate. in a Newtonian field is considered. New analytic solutions are obtained for plane intermediate-thrust arcs, using the canonical system of equations of the variational problem and the properties of the switching function. These solutions represent certain spiral trajectories. In motion with a fixed time, at arbitrary angular distances, these solutions satisfy Robbins' necessary optimum condition. As an example the problem of minimizing the characteristic Velocity of flight between elliptic orbits is considered.

V. G. Petukhov - One of the best experts on this subject based on the ideXlab platform.

  • Application of the Angular Independent Variable and Its Regularizing Transformation in the Problems of Optimizing Low-Thrust Trajectories
    Cosmic Research, 2019
    Co-Authors: V. G. Petukhov
    Abstract:

    — The expediency of using the true longitude or the associated angle as an independent variable in the problems of optimizing multi-revolution, low-thrust trajectories of spacecraft is considered. The auxiliary longitude is introduced, which is used further as a new independent variable instead of time. The advantage of using the auxiliary longitude as an independent variable in the problem of optimizing the trajectories with a fixed angular range and optimum transfer time is demonstrated. The problems of optimizing the trajectories of spacecraft with an ideally controlled, limited-power engine and a limited-thrust engine with a Constant Exhaust Velocity are considered. The possibility of improving the convergence of the methods of solving the problems of optimizing the trajectories with a limited-thrust engine is considered. This improvement is achieved by joint utilization of the smoothing approximation of a relay thrust-switching function and the regularizing transformation of an independent variable, which extends the switching function values in the vicinity of thrust switching instants. Based on the results, the method for solving the problems of optimizing multi-revolution transfers is proposed; the numerical examples of its application are presented.

  • Joint Optimization of Control and Main Trajectory and Design Parameters of an Interplanetary Spacecraft with an Electric Propulsion System
    Cosmic Research, 2019
    Co-Authors: V. G. Petukhov, A. V. Ivanyukhin, Woo Sang Wook
    Abstract:

    — The problem of joint optimization of thrust vector control programs and main trajectory and design parameters of an interplanetary spacecraft with an electric propulsion system (EPS) is studied. The purpose of optimization is maximizing the useful spacecraft mass. For mathematical models of a controlled-in-thrust and single-mode EPS with a Constant Exhaust Velocity and for a fixed duration of transfer over a heliocentric trajectory, the necessary conditions are obtained for joint optimality of: (a) thrust vector control, (b) departure hyperbolic Velocity excess vector, (c) departure date, (d) EPS specific impulse, (e) maximum EPS power, and (f) maximum power of spacecraft’s power supply system. It is shown that, for some problems of practical interest, the optimum value of EPS thrust is equal to its minimum permissible value. The results can be of interest at the early stages of designing an interplanetary spacecraft with EPS and for justifying the choice of main parameters of developed electric propulsion thrusters.

  • The thrust minimization problem and its applications
    Cosmic Research, 2015
    Co-Authors: A. V. Ivanyukhin, V. G. Petukhov
    Abstract:

    An indirect approach to the optimization of trajectories with finite thrust based on Pontryagin’s maximum principle is discussed. The optimization is aimed at calculating the minimum thrust for a point-to-point flight completed within a given interval of time with a Constant Exhaust Velocity and a Constant power. This may help calculate the region of existence of the optimum trajectory with thrust switching: it is evident that the latter problem may be solved if minimum thrust is lower than or equal to the available thrust in the problem with switching. A technique for calculating the optimum trajectories with a finite thrust by solving the problem of minimization of the thrust acceleration with a subsequent numerical continuation with respect to the mass flow towards the thrust minimization problem is proposed. This technique offers an opportunity to detect degeneracies associated with the lack of thrust or specific impulse. In effect, it allows one to calculate the boundaries of the region of existence of trajectories with thrust switching and thus makes it possible to automate the process of solving the problem of optimization of trajectories with thrust switching.

Fernando A. Sanabria - One of the best experts on this subject based on the ideXlab platform.

  • Extremal Control and Guidance Solutions for Orbital Transfer with Intermediate Thrust
    The Journal of the Astronautical Sciences, 2015
    Co-Authors: Dilmurat M. Azimov, Fernando A. Sanabria
    Abstract:

    Mayer’s variational problem of determining optimal trajectories of motion with Constant Exhaust Velocity and limited mass-flow rate in a Newtonian field is considered. Analytical solutions for extremal transfers between two coplanar elliptical orbits via one and two intermediate-thrust arcs are presented. It is shown that in the cases of transfers via one and two intermediate-thrust arcs, the orbital parameters have to satisfy respectively two constraints and one constraint imposed by the continuity conditions formed at the junctions. This means that respectively two and one of these orbital parameters must not be arbitrary. Furthermore, by utilizing the analytical solutions for the intermediate-thrust arcs, the corresponding extremal guidance laws for a transfer between two points with arbitrary position vectors and for a transfer between elliptical orbits are presented. The guidance commands are formulated in terms of commanded thrust angle and commanded mass-flow rate. A numerical example illustrating the proposed trajectory and guidance solutions is discussed. The results of the computations are compared to those of similar one- and two- impulsive transfers, and a low-thrust orbit raising maneuver. It is demonstrated that for some eccentricities of the terminal orbits, the fuel consumption for a transfer via an intermediate-thrust arc is comparable to that of the two-impulsive transfers. Analyses show that a maneuver with such an arc may be fuel-efficient with longer duration and higher thrust than that of the low-thrust maneuver. The trajectory computations and guidance performances are illustrated by graphical relationships.

Robert H. Bishop - One of the best experts on this subject based on the ideXlab platform.

  • Extremal Rocket Motion with Maximum Thrust in a Linear Central Field
    Journal of Spacecraft and Rockets, 2001
    Co-Authors: Dilmurat M. Azimov, Robert H. Bishop
    Abstract:

    TheMayer variationalproblem of determining optimal trajectories of a rocket movingwith maximumthrust in a thin spherical layer within a central Newtonian Ž eld is considered. The present work is devoted to the analytical investigation of maximum thrust arcs for a rocket engine with Constant Exhaust Velocity and limited mass  ow rate using the necessary conditions of optimality.Many problems of practical interest admit an approximation of the central Newtonian Ž eld by a linear central Ž eld. It is shown that the linear central Ž eld assumption is valid when the thrust vector is nearly tangential to the orbit and the rocket remains in a sufŽ ciently thin spherical layer during the maneuver. When the linear central Ž eld approximationis utilized, analytic closed-form expressions are obtained describing optimal maximum thrust space trajectories. The problem of optimal orbit transfer between coplanar circular orbits is considered to illustrate the solution process, which comprises two maximumthrust and three null thrust arcs. It is shown that solutionsof the problem are comparablewith solutionsbased on assumptions of instantaneous changes in Velocity, including the Hohmann transfer.

Daniel V. Macinnis - One of the best experts on this subject based on the ideXlab platform.

  • A Review and Discussion of Rocket Vehicle Propulsion Efficiency
    50th AIAA Aerospace Sciences Meeting including the New Horizons Forum and Aerospace Exposition, 2012
    Co-Authors: Mark T. Langhenry, James K. Villarreal, Daniel V. Macinnis
    Abstract:

    The efficiency with which any system uses available energy is often an important measure of the performance of that system. Rockets operate by transforming carried energy of various forms into useful kinetic energy of the payload portion of the vehicle. The efficiency of this transformation is usually not examined in favor of maximizing the change in Velocity, V, of the rocket vehicle. However, missions such as launch vehicles, interplanetary missions or other complex trajectories where the initial mass of the vehicle is a large economic driver may benefit from more efficiently expending the energy that is required to be carried. A review of rocket propulsion efficiency is presented. Various definitions of efficiency are discussed such as optimizing the end kinetic energy of the vehicle as a function of mass ratio or optimizing the end kinetic energy as a function of total energy carried. It is shown through derivations of the V equation with changing Exhaust Velocity during the rocket operation that increases in V may be achieved over the Constant Exhaust Velocity case. For a given amount of propellant energy the optimum manner in which propellant should be expelled is discussed. The potential magnitude of the increase in V is shown through example calculations. The discussion is expanded to a volume limited chemical rocket system where the Exhaust Velocity depends on the mixture ratio of the oxidizer and fuel. Increases in V are shown by example calculations with various restrictions on propellant loading.