A non-exhaustive restatement of the angular momentum reduction in the three-body problem

1973 ◽  
Vol 33 (2) ◽  
pp. 243-266 ◽  
Author(s):  
E. El Baz ◽  
C. Fayard ◽  
G -H. Lamot ◽  
J. Pigeon
Keyword(s):  
Angular Momentum ◽  
Body Problem ◽  
Three Body Problem ◽  
Three Body

SEPARATION OF ROTATIONAL DEGREES OF FREEDOM IN A QUANTUM THREE-BODY PROBLEM

2001 ◽  
Vol 10 (01) ◽  
pp. 69-82 ◽  
Author(s):  
XIAO-YAN GU ◽  
BIN DUAN ◽  
ZHONG-QI MA
Keyword(s):  
Angular Momentum ◽  
Degrees Of Freedom ◽  
Body Problem ◽  
Three Body Problem ◽  
Radial Functions ◽  
Base Functions ◽  
Rotational Degrees Of Freedom ◽  
Three Body ◽  
The Given

We demonstrate explicitly how the rotational degrees of freedom in a quantum three-body problem is separated completely from the internal ones. It is shown that only finite partial angular momentum states are involved in constructing the base-functions with the given angular momentum and parity, and the contributions by the remaining partial angular momentum states are incorporated into the contributions by the generalized radial functions.

Sum rules in a three-body problem at fixed angular momentum

1989 ◽  
Vol 17 (4) ◽  
pp. 307-313 ◽  
Author(s):  
S. P. Merkuriev ◽  
A. A. Kvitsinsky
Keyword(s):  
Angular Momentum ◽  
Body Problem ◽  
Sum Rules ◽  
Three Body Problem ◽  
Three Body

Faddeev approach to the three-body problem in total-angular-momentum representation

1989 ◽  
Vol 6 (2) ◽  
pp. 97-113 ◽  
Author(s):  
V. V. Kostrykin ◽  
A. A. Kvitsinsky ◽  
S. P. Merkuriev
Keyword(s):  
Angular Momentum ◽  
Total Angular Momentum ◽  
Body Problem ◽  
Momentum Representation ◽  
Three Body Problem ◽  
Three Body

The zero angular momentum, three-body problem: All but one solution has syzygies

2007 ◽  
Vol 27 (6) ◽  
pp. 1933-1946 ◽  
Author(s):  
RICHARD MONTGOMERY
Keyword(s):  
Angular Momentum ◽  
Body Problem ◽  
Three Body Problem ◽  
Mass Ratios ◽  
Three Body

AbstractA syzygy in the three-body problem is a collinear instant. We prove that, with the exception of Lagrange’s solution, every solution to the zero angular momentum, Newtonian three-body problem suffers syzygies. The proof works for all mass ratios.

scholarly journals A SURVEY ON EXTENSIONS OF THE PURE GRAVITY SWING-BY MANEUVER

2021 ◽  
Vol 57 (2) ◽  
pp. 445-457
Author(s):  
A. F. S. Ferreira ◽  
R. V. de Moraes ◽  
A. F. B. A. Prado ◽  
O. C. Winter ◽  
V. M. Gomes
Keyword(s):  
Angular Momentum ◽  
Mathematical Models ◽  
Numerical Simulations ◽  
Body Problem ◽  
Restricted Three Body Problem ◽  
Three Body Problem ◽  
Pure Gravity ◽  
Celestial Bodies ◽  
Patched Conics ◽  
Three Body

The present paper surveys the more recent techniques related to the swingby maneuver, where a spacecraft changes its energy and angular momentum by passing close to celestial bodies. It is focused on the literature related to extensions of this maneuver, with emphasis in the powered version, where an impulse is applied to the spacecraft near the closest approach. Several mathematical models are considered, including the patched-conics approximation for analytical studies, and the restricted three-body problem for the numerical simulations. The main goal is to show the models and the main conclusions available in the literature for those maneuvers. Some key results are shown to discuss important aspects of this maneuver, including the analysis of the energy variation of the spacecraft, the behavior of the trajectories and other applications.

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