A mathematical study of the tethered slingshot maneuver using the elliptic restricted problem

2020 ◽  
Vol 102 (3) ◽  
pp. 1585-1609
Author(s):  
Alessandra F. S. Ferreira ◽  
Rodolpho V. Moraes ◽  
Antônio F. B. A. Prado ◽  
Othon C. Winter
Keyword(s):  
Restricted Problem ◽  
Mathematical Study ◽  
Elliptic Restricted Problem

scholarly journals The Mechanism of Branching of Three-Dimensional Periodic Orbits from the Plane

1983 ◽  
Vol 74 ◽  
pp. 213-224
Author(s):  
I.A. Robin ◽  
V.V. Markellos
Keyword(s):  
Recent Work ◽  
Periodic Orbits ◽  
Restricted Problem ◽  
Three Dimensional ◽  
General Situation ◽  
Orbital Symmetry ◽  
Resonant Orbits ◽  
Symmetry Properties ◽  
Elliptic Restricted Problem ◽  
Symmetric Periodic Orbits

AbstractA linearised treatment is presented of vertical bifurcations of symmetric periodic orbits(bifurcations of plane with three-dimensional orbits) in the circular restricted problem. Recent work on bifurcations from vertical-critical orbits (av = ±1) is extended to deal with the v more general situation of bifurcations from vertical self-resonant orbits (av = cos(2Πn/m) for integer m,n) and it is shown that in this more general case bifurcating families of three-dimensional orbits always occur in pairs, the orbital symmetry properties being governed by the evenness or oddness of the integer m. The applicability of the theory to the elliptic restricted problem is discussed.

On the elliptic restricted problem of three bodies

1964 ◽  
Vol 69 ◽  
pp. 230 ◽  
Author(s):  
Victor Szebehely ◽  
Giorgio E. O. Giacaglia
Keyword(s):  
Restricted Problem ◽  
Elliptic Restricted Problem
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