Optimal Space Trajectories—A Review of Published Work

1968 ◽  
Vol 72 (686) ◽  
pp. 141-146 ◽  
Author(s):  
D. J. Bell
Keyword(s):  
Gravitational Field ◽  
General Theory ◽  
Optimal Trajectory ◽  
Space Vehicle ◽  
Two Dimensions ◽  
Performance Criteria ◽  
Space Vehicles ◽  
Optimal Space Trajectories ◽  
End Conditions ◽  
Optimal Space

The problem of transferring a space vehicle between two points in a given gravitational field such that the minimum amount of fuel is used has been called the fundamental navigational problem of astronautics. In such a problem it may be required to find the optimum thrust magnitude and thrust direction which yields a minimum fuel trajectory. Furthermore, certain end conditions may be specified which the optimal trajectory must satisfy. In a large number of published papers the velocity of the vehicle is supposed known both at the beginning of the transfer and at the end whereas the time taken to complete the manoeuvre may or may not be given. Also, other performance criteria have been chosen besides minimum fuel. For example, minimum time of transit or maximum orbital altitude at perigee. Papers mentioned in this review deal mainly with flight in two dimensions apart from those sections on general theory. Furthermore, all space vehicles considered are assumed to have a fixed exhaust velocity unless otherwise stated.

Theory of Electron Diffraction by Crystals

1967 ◽  
Vol 22 (4) ◽  
pp. 422-431 ◽  
Author(s):  
Kyozaburo Kambe
Keyword(s):  
Integral Equation ◽  
Electron Diffraction ◽  
General Theory ◽  
Green’S Function ◽  
Green's Function ◽  
Scattering Problem ◽  
Three Dimensional ◽  
Two Dimensions ◽  
The Third ◽  
Third Dimension

A general theory of electron diffraction by crystals is developed. The crystals are assumed to be infinitely extended in two dimensions and finite in the third dimension. For the scattering problem by this structure two-dimensionally expanded forms of GREEN’S function and integral equation are at first derived, and combined in single three-dimensional forms. EWALD’S method is applied to sum up the series for GREEN’S function.

Relativistic synchronization of onboard clocks of navigation space vehicles with the aid of intersatellite measurements

2021 ◽  
pp. 56-66
Author(s):  
Nikolay N. Vasilyuk ◽  
Alexander P. Chervonkin
Keyword(s):  
Proper Time ◽  
Space Vehicle ◽  
Relativistic Correction ◽  
Point Of View ◽  
Space Vehicles ◽  
Satellite Measurements ◽  
Clock Drift ◽  
Coordinate Time ◽  
Upper Limit ◽  
Unambiguous Interpretation

The problem of the synchronization of onboard clocks of navigation satellites has considered from a relativistic point of view using the concept of “coordinate simultaneity”. This concept allows an unambiguous interpretation of the synchronization results within the framework of general relativity. The algorithm of intersatellite measurements processing has formulated in terms of a proper time of a space vehicle and the coordinate time of a reference frame. Rules of transformation between coordinate and proper time scales have indicated. An analytical expression has obtained for the periodic relativistic correction to the estimated value of the relative clock drift. This correction has expressed in terms of the coordinate time of a ground observer. The value of this correction exceeds the acceptable synchronization error and should be taken into account for the inter-satellite measurements processing. The error of the relativistic correction determination has calculated. This error provides an upper limit for the period of uploading of ephemeris data on the board of the space vehicle.

The General Theory of Relativity

2017 ◽  
Author(s):  
Hanoch Gutfreund ◽  
Jürgen Renn
Keyword(s):  
General Relativity ◽  
Gravitational Field ◽  
General Theory ◽  
Reference Frames ◽  
Mathematical Formulation ◽  
Rotating Disk ◽  
Theory Of Relativity ◽  
Relativity Principle ◽  
Non Euclidean Geometry ◽  
Physical Laws

This chapter shows how Einstein has developed and described the mathematical apparatus that is necessary to formulate the physical contents of the general theory of gravity. It first discusses the transition from the special to the general relativity principle. According to Einstein's understanding of such a general relativity principle, physical laws are independent of the state of motion of the reference space in which they are described. The chapter argues that such a generalization of the relativity principle to include accelerated reference frames is possible because all inertial effects caused by acceleration can be alternatively attributed to the presence of a gravitational field. The model of a rotating disk is then used to show that general relativity implies non-Euclidean geometry and that the gravitational field is represented by curved spacetime. After the introduction of these basic concepts and principles, the chapter presents the mathematical formulation of the theory.

Free Response of an Array of Mono-Coupled Elements Terminating at General Boundaries

1996 ◽  
Vol 15 (2) ◽  
pp. 89-98 ◽  
Author(s):  
A.S. Bansal
Keyword(s):  
General Theory ◽  
Natural Frequencies ◽  
Free Response ◽  
Frequency Dependent ◽  
Periodic Arrays ◽  
Vibrational Response ◽  
End Conditions ◽  
Mass Damper ◽  
Simple Supports ◽  
Set Up

Receptance methods have been used to set up general equations that govern the vibrational response of a finite array of N mono-coupled elements terminating at general boundaries. The equations have been modified to introduce ideal and the frequency dependent boundary conditions offered by semi-infinite periodic arrays attached at its ends. The general theory has been adapted to determine the natural frequencies of some finite 5-span beams on simple supports with their ends having various combinations of ideal and frequency dependent end conditions. Lowest group of natural frequencies of the finite beams having different disorders and different combinations of ideal, elastic and dissipative boundaries have been computed and discussed. The conditions under which the undamped combined systems can behave like spring-mass systems and spring-mass-damper systems have also been identified and explained.

Multidimensional performance evaluation styles: budget rigidity and discretionary adjustments

2020 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
Keita Masuya ◽  
Eisuke Yoshida
Keyword(s):  
Performance Evaluation ◽  
Empirical Analysis ◽  
Environmental Uncertainty ◽  
Two Dimensions ◽  
Performance Evaluations ◽  
Performance Criteria ◽  
Content Type ◽  
Ex Post ◽  
Performance Effects ◽  
The Empirical Analysis

Purpose This study aims to reconceptualize performance evaluation styles and reveal their performance effects. Design/methodology/approach Based on a literature review, this study conceptualizes performance evaluation styles on two dimensions: priority of budgetary targets when setting performance criteria and use of accounting information for ex-post performance evaluation. This study discusses two concepts – budget rigidity and discretionary adjustments – to explain these two dimensions, and their optimal combination is then investigated by considering environmental uncertainty. The empirical analysis uses survey data from Japanese firms. Findings The results indicate that suitable combinations of budget rigidity and discretionary adjustments differ depending on environmental uncertainty. As expected, a combination of lower budget rigidity and higher discretionary adjustments is optimal in an uncertain environment. Contrary to expectations, a combination of higher budget rigidity and higher discretionary adjustments is optimal in a stable environment. Moreover, higher discretionary adjustments complement budgetary targets’ motivational effects, regardless of environmental uncertainty. Originality/value This study’s theoretical and empirical analysis suggests that it is difficult to understand the performance implications of performance evaluation styles without recognizing their multidimensionality and interdependencies. Moreover, the results demonstrate that discretionary adjustments in budget-based performance evaluations seem to act rationally in practice.

Reduced Transversality Conditions in Optimal Space Trajectories

2013 ◽  
Vol 36 (5) ◽  
pp. 1289-1300 ◽  
Author(s):  
Binfeng Pan ◽  
Zheng Chen ◽  
Ping Lu ◽  
Bo Gao
Keyword(s):  
Space Trajectories ◽  
Transversality Conditions ◽  
Optimal Space Trajectories ◽  
Optimal Space
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