A note on the asymptotic behavior in angular momentum for Potential Theory

1965 ◽  
Vol 37 (4) ◽  
pp. 1747-1748 ◽  
Author(s):  
M. Scadron ◽  
J. Wright
Keyword(s):  
Asymptotic Behavior ◽  
Angular Momentum ◽  
Potential Theory

scholarly journals Particular superintegrability of 3-body (modified) Newtonian gravity

2020 ◽  
Vol 35 (22) ◽  
pp. 2050185
Author(s):  
Alexander V. Turbiner ◽  
Juan Carlos Lopez Vieyra
Keyword(s):  
Angular Momentum ◽  
Potential Theory ◽  
Total Angular Momentum ◽  
Newtonian Gravity ◽  
Constants Of Motion ◽  
Body Potential ◽  
Poisson Commute

It is found explicitly 5 Liouville integrals in addition to total angular momentum which Poisson commute with Hamiltonian of 3-body Newtonian Gravity in [Formula: see text] along the remarkable figure-8-shape trajectory discovered by Moore-Chenciner-Montgomery. It is verified that they become constants of motion along this trajectory. Hence, 3-body choreographic motion on figure-8-shape trajectory in [Formula: see text] Newtonian gravity (Moore, 1993), as well as in [Formula: see text] modified Newtonian gravity by Fujiwara et al., is maximally superintegrable. It is conjectured that any 3-body potential theory that admits Figure-8-shape choreographic motion is superintegrable along the trajectory.

Asymptotic Behavior of theSMatrix for High Angular Momentum

1963 ◽  
Vol 129 (6) ◽  
pp. 2818-2823 ◽  
Author(s):  
A. M. Jaffe ◽  
Y. S. Kim
Keyword(s):  
Asymptotic Behavior ◽  
Angular Momentum ◽  
High Angular Momentum
Sign in / Sign up

Export Citation Format

Share Document