Open AccessA simple derivation and interpretation of the third integral in stellar dynamics
Author(s) -
LyndenBell D.
Publication year - 2003
Publication title -
monthly notices of the royal astronomical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 2.058
H-Index - 383
eISSN - 1365-2966
pISSN - 0035-8711
DOI - 10.1046/j.1365-8711.2003.06041.x
Subject(s) - physics , simple (philosophy) , scalar (mathematics) , interpretation (philosophy) , classical mechanics , product (mathematics) , integral equation , dynamics (music) , theoretical physics , mathematical physics , mathematical analysis , geometry , mathematics , philosophy , epistemology , computer science , programming language , acoustics
Starting from the problem of two fixed centres we find a simple derivation of its third integral in terms of the scalar product of the angular momenta about the two fixed centres. This is then generalized to find the general form of the potential in which an exact third integral exists.