Generalized Lagrangian orbital elements for central force problems

1985 ◽  
Vol 36 (1) ◽  
pp. 71-82 ◽  
Author(s):  
Patrick G. Whitman ◽  
John J. Matese
Keyword(s):  
Central Force ◽  
Orbital Elements ◽  
Generalized Lagrangian ◽  
Central Force Problems

scholarly journals Symmetries in central-force problems

2003 ◽  
pp. 47-52 ◽  
Author(s):  
V. Mioc ◽  
M. Barbosu
Keyword(s):  
Vector Fields ◽  
Body Problem ◽  
Blow Up ◽  
Central Force ◽  
Polar Coordinates ◽  
Global Flow ◽  
Two Body Problem ◽  
Concrete Problem ◽  
Central Force Problems ◽  
Force Problem

The two-body problem in central fields (reducible to a central-force problem) models a lot of concrete astronomical situations. The corresponding vector fields (in Cartesian and polar coordinates, extended via collision-blow-up and infinity-blow-up transformations) exhibit nice symmetries that form eight-element Abelian groups endowed with an idempotent structure. All these groups are isomorphic, which is not a trivial result, given the different structures of the corresponding phase spaces. Each of these groups contains seven four-element subgroups isomorphic to Klein?s group. These symmetries are of much help in understanding various characteristics of the global flow of the general problem or of a concrete problem at hand, and are essential in searching for periodic orbits.

Central Force Problems

2018 ◽  
pp. 111-152
Author(s):  
Matthew J. Benacquista ◽  
Joseph D. Romano
Keyword(s):  
Central Force ◽  
Central Force Problems

An algebraic method for solving central force problems

2002 ◽  
Vol 70 (9) ◽  
pp. 945-950 ◽  
Author(s):  
T. H. Cooke ◽  
J. L. Wood
Keyword(s):  
Algebraic Method ◽  
Central Force ◽  
Central Force Problems

scholarly journals Symmetry reduction for central force problems

2016 ◽  
Vol 37 (5) ◽  
pp. 055003
Author(s):  
Robert I McLachlan ◽  
Klas Modin ◽  
Olivier Verdier
Keyword(s):  
Symmetry Reduction ◽  
Central Force ◽  
Central Force Problems
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