Analytical Study of the Primer Vector and Orbit Transfer Switching Function

2010 ◽  
Vol 33 (1) ◽  
pp. 235-245 ◽  
Author(s):  
Brian Roger Jamison ◽  
Victoria Coverstone
Keyword(s):  
Analytical Study ◽  
Switching Function ◽  
Orbit Transfer ◽  
Primer Vector

Improving a Nonoptimal Impulsive Trajectory

2018 ◽  
Author(s):  
John E. Prussing
Keyword(s):  
Necessary Conditions ◽  
Optimal Solution ◽  
Fixed Time ◽  
Orbit Transfer ◽  
Primer Vector ◽  
The Way

Improving a nonoptimal trajectory is analysed, including adding terminal coasts and midcourse impulses in fixed-time trajectories. Orbit transfer is also analysed. If the primer vector evaluated along an impulsive trajectory fails to satisfy the necessary conditions (NC) for an optimal solution, the way in which the NC are violated provides information that can lead to a solution that does satisfy the NC. The necessary gradients were first derived by Lion and Handelsman.

scholarly journals Solving Coplanar Power-Limited Orbit Transfer Problem by Primer Vector Approximation Method

2012 ◽  
Vol 2012 ◽  
pp. 1-9 ◽  
Author(s):  
Weijun Huang
Keyword(s):  
Vector Function ◽  
Approximation Method ◽  
Transfer Problem ◽  
Approximate Solutions ◽  
Orbit Transfer ◽  
Numerical Tests ◽  
Vector Approximation ◽  
Primer Vector

The coplanar orbit transfer problem has been an important topic in astrodynamics since the beginning of the space era. Though many approximate solutions for power-limited orbit transfer problem have been developed, most of them rely on simplifications of the dynamics of the problem. This paper proposes a new approximation method called primer vector approximation method to solve the classic power-limited orbit transfer problem. This method makes no simplification on the dynamics, but instead approximates the optimal primer-vector function. With this method, this paper derives two approximate solutions for the power-limited orbit transfer problem. Numerical tests show the robustness and accuracy of the approximations.

scholarly journals How Many Impulses Redux

2019 ◽  
Vol 67 (2) ◽  
pp. 257-334 ◽  
Author(s):  
Ehsan Taheri ◽  
John L. Junkins
Keyword(s):  
Significant Contribution ◽  
Rocket Engine ◽  
Switching Function ◽  
Orbit Transfer ◽  
Switching Surface ◽  
Fuel Switching ◽  
Time Profiles ◽  
Total Impulse ◽  
Finite Thrust ◽  
High Thrust

AbstractA central problem in orbit transfer optimization is to determine the number, time, direction, and magnitude of velocity impulses that minimize the total impulse. This problem was posed in 1967 by T. N. Edelbaum, and while notable advances have been made, a rigorous means to answer Edelbaum’s question for multiple-revolution maneuvers has remained elusive for over five decades. We revisit Edelbaum’s question by taking a bottom-up approach to generate a minimum-fuel switching surface. Sweeping through time profiles of the minimum-fuel switching function for increasing admissible thrust magnitude, and in the high-thrust limit, we find that the continuous thrust switching surface reveals the N-impulse solution. It is also shown that a fundamental minimum-thrust solution plays a pivotal role in our process to determine the optimal minimum-fuel maneuver for all thrust levels. Remarkably, we find that the answer to Edelbaum’s question is not generally unique, but is frequently a set of equal-Δv extremals. We further find, when Edelbaum’s question is refined to seek the number of finite-duration thrust arcs for a specific rocket engine, that a unique extremal is usually found. Numerical results demonstrate the ideas and their utility for several interplanetary and Earth-bound optimal transfers that consist of up to eleven impulses or, for finite thrust, short thrust arcs. Another significant contribution of the paper can be viewed as a unification in astrodynamics where the connection between impulsive and continuous-thrust trajectories are demonstrated through the notion of optimal switching surfaces.

scholarly journals Symmetry Properties of Optimal Relative Orbit Trajectories

2015 ◽  
Vol 2015 ◽  
pp. 1-11 ◽  
Author(s):  
Mauro Pontani
Keyword(s):  
Symmetry Property ◽  
Minimum Time ◽  
Three Dimensions ◽  
Switching Function ◽  
Primer Vector Theory ◽  
Relative Orbit ◽  
Symmetry Properties ◽  
Primer Vector ◽  
Vector Theory

The determination of minimum-fuel or minimum-time relative orbit trajectories represents a classical topic in astrodynamics. This work illustrates some symmetry properties that hold for optimal relative paths and can considerably simplify their determination. The existence of symmetry properties is demonstrated in the presence of certain boundary conditions for the problems of interest, described by the linear Euler-Hill-Clohessy-Wiltshire equations of relative motion. With regard to minimum-fuel paths, the primer vector theory predicts the existence of several powered phases, divided by coast arcs. In general, the optimal thrust sequence and duration depend on the time evolution of the switching function. In contrast, a minimum-time trajectory is composed of a single continuous-thrust phase. The first symmetry property concerns minimum-fuel and minimum-time orbit paths, both in two and in three dimensions. The second symmetry property regards minimum-fuel relative trajectories. Several examples illustrate the usefulness of these properties in determining minimum-time and minimum-fuel relative paths.

Illustration of the primer vector in time- fixed, orbit transfer.

AIAA Journal ◽  
1969 ◽  
Vol 7 (6) ◽  
pp. 1167-1168 ◽  
Author(s):  
JOHN E. PRUSSING
Keyword(s):  
Orbit Transfer ◽  
Primer Vector

Application of information theory to switching function minimisation

1990 ◽  
Vol 137 (5) ◽  
pp. 389 ◽  
Author(s):  
A.M. Kabakçioḡlu ◽  
P.K. Varshney ◽  
C.R.P. Hartmann
Keyword(s):  
Information Theory ◽  
Switching Function

Analytical Study of Violence Theme in Victoria Schwab’s This Savage Song

2019 ◽  
Keyword(s):  
Analytical Study ◽  
Research Paper ◽  
The Novel ◽  
Vicious Cycle ◽  
Aggressive Approach ◽  
Research Article ◽  
The People ◽  
The Social ◽  
Different Dimensions ◽  
The Right

This research article focuses on the theme of violence and its representation by the characters of the novel “This Savage Song” by Victoria Schwab. How violence is transmitted through genes to next generations and to what extent socio- psycho factors are involved in it, has also been discussed. Similarly, in what manner violent events and deeds by the parents affect the psychology of children and how it inculcates aggressive behaviour in their minds has been studied. What role is played by the parents in grooming the personality of children and ultimately their decisions to choose the right or wrong way has been argued. In the light of the theory of Judith Harris, this research paper highlights all the phenomena involved: How the social hierarchy controls the behaviour. In addition, the aggressive approach of the people in their lives has been analyzed in the light of the study of second theorist Thomas W Blume. As the novel is a unique representation of supernatural characters, the monsters, which are the products of some cruel deeds, this research paper brings out different dimensions of human sufferings with respect to these supernatural beings. Moreover, the researcher also discusses that, in what manner the curse of violence creates an inevitable vicious cycle of cruel monsters that makes the life of the characters turbulent and miserable.

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