Three-Dimensional Optimum Thrust Trajectories for Power Limited Propulsion Systems

Melbourne, W. G.

doi:10.2514/8.5902

Cited by 30 publications

(22 citation statements)

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“…The corresponding variational problem of flight dynamics on the determination of optimal trajectories of a rocket moving with a constant exit velocity and bounded mass flow rate in a Newton field is known as the Lawden problem [2]. The optimal trajectory may contain three types of arcs: null-thrust (NT), intermediate-thrust (NT), and maximum-thrust (MT) arcs.…”

Section: Problems With Parameters Of Propulsion Systemsmentioning

confidence: 99%

“…Equations of such trajectories and optimal thrust, including the shape of the functional, are derived by Irving [8]. Earlier works of Melbourne and Sauer deal with constant and variable thrusts [2,27]. Variational equations contained constraints on power and exit velocity.…”

Section: Low-thrust Trajectoriesmentioning

confidence: 99%

“…Methods of construction of optimal LT trajectories for space vehicles equipped with low-thrust engines are studied in [2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17]. Equations of such trajectories and optimal thrust, including the shape of the functional, are derived by Irving [8].…”

Section: Low-thrust Trajectoriesmentioning

confidence: 99%

“…Ishlinskii, and others. Papers devoted to optimal rocket motion in a central Newton field have theoretical and practical importance [1,2]. The corresponding variational problem and the specifics of the methods of its solution are pivotal.…”

Section: Introductionmentioning

confidence: 99%

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Active Rocket Trajectory Arcs: A Review

Azimov

2005

Autom Remote Control

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This paper reviews the development of analytical, approximate analytical, and numerical methods for solving the variational problem on the determination of optimal rocket trajectories in gravitational fields, and their application to study flight dynamics. Specifics of these methods as applied to solve modern and complex problems are described. A variational problem is formulated and extremal thrust arcs are described. Papers containing results of analytical investigations on thrust arcs are reviewed in depth. Partially investigated problems are described. Problems of great interest in the development of methods for solving the variational problem and problems in the theory of optimal trajectories are mentioned.

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Section: Problems With Parameters Of Propulsion Systemsmentioning

confidence: 99%

Section: Low-thrust Trajectoriesmentioning

confidence: 99%

Section: Low-thrust Trajectoriesmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Active Rocket Trajectory Arcs: A Review

Azimov

2005

Autom Remote Control

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“…In Ref. 1, there appeared the results from a series of trajectories to the planets Venus and Mars. An optimum variable thrust program was used to generate these trajectories.…”

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confidence: 97%

Optimum Interplanetary Rendezvous With Power-Limited Vehicles

Melbourne

Sauer

1963

AIAA Journal

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The optimum thrust programs for power-limited propulsion systems are used to generate rendezvous trajectories from Earth to Mars for various flight times and launch dates during the years 1968 to 1971. The manner in which the propulsion requirements vary with flight time and launch date is considered, and a comparison of vehicle performance using the variable and constant thrust programs is presented. The existence of optimum launch dates is interpreted in terms of certain transversality conditions derivable from the calculus of variations. A brief comparison of the advanced propulsion vehicle and the ballistic vehicle propulsion requirements is made for Earth-Mars rendezvous trajectories.T HE emergence of advanced propulsion for interplanetary flights has generated great interest in the application of optimization theory to advanced propulsion vehicle systems and to trajectory design. It becomes necessary to obtain fairly accurate estimates of the payload capabilities of advanced propulsion vehicles for various interplanetary missions. In Ref. 1, there appeared the results from a series of trajectories to the planets Venus and Mars. An optimum variable thrust program was used to generate these trajectories. Moreover, certain terminal conditions, such as the orientation of the terminal orbit and the terminal position on the orbit, were left unspecified, and corresponding transversality conditions derived from the calculus of variations were satisfied instead.This paper is concerned with the problem in which all end conditions, as determined by the planetary ephemerides, are specified, and the main purpose is to show the manner in which the propulsion requirements vary both with flight time and with launch date. This procedure is analogous to the problem in ballistic trajectories in which the velocity increments required for interplanetary missions are determined (2,3). 3 In advanced propulsion trajectories, however, the propulsion intervals constitute a significant portion of the trajectory, and, therefore, the thrust program employed becomes quite important in payload studies, and optimization theory as applied to the trajectory analysis is of considerable use. A comparison of vehicle performance will be made between the use of an optimum variable thrust program and the use of an optimum constant thrust program. Optimum Thrust EquationsIn order to develop an optimum thrust program that extremizes some terminal quantity indicative of vehicle performance, it is necessary to include the constraints of the system. For the power-limited propulsion system, the constraints are the equations of motion of the vehicle and an equation describing the fact that the amount of kinetic power contained in the exhaust propellant is constrained. Generally, the kinetic power depends on the efficiency of power conversion from the nuclear powerplant of the vehicle, and the efficiency, in turn, is dependent on the exhaust velocity employed. In this treatment, the kinetic power is constant, which is the case for the constant thrust pro...

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Rößger¹,

Zehle²

1963

Grundlagen Der Raumfahrzeugführung

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Three-Dimensional Optimum Thrust Trajectories for Power Limited Propulsion Systems

Cited by 30 publications

References 0 publications

Active Rocket Trajectory Arcs: A Review

Active Rocket Trajectory Arcs: A Review

Optimum Interplanetary Rendezvous With Power-Limited Vehicles

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