Abstract
The disappearance of some integrals of motion when two or more resonance conditions are approached at the same time is explained. As an example a Hamiltonian of three degrees of freedom is considered in action-angle variables which in zero order represents three harmonic oscillators, while the perturbation contains two trigonometric terms. One integral disappears if two appropriate resonant conditions are approached sufficiently closely.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Barbanis, B.: 1966,Astron. J. 71, 415.
Contopoulos, G.: 1966,Astrophys. J. Suppl. 13, 503.
Contopoulos, G.: 1968,Astrophys. J. 153, 83.
Contopoulos, G.: 1974, in D. Kotsakis (ed.), Volume in h. S. Placidis, Athens, p. 139.
Contopoulos, G.: 1975,IAU Symp. 69, 209.
Ford, J.: 1975, in E. D. G. Cohen (ed.),Fundamental Problems in Statistical Mechanics, Vol. 3, p. 215, North-Holland, Amsterdam.
Giorgilli, A. and Galgani, L.: 1978,Celest. Mech. (in press).
Froeschlé, C. and Scheidecker, J. P. 1973,Astrophys. Space Sci. 25, 373.
Gustavson, F. G., 1966,Astron. J. 71, 670.
Hénon, M. and Heiles, C.: 1964,Astron J. 69, 73.
Kummer, M.: 1975,J. Math. Anal. Appl. 52, 64.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Contopoulos, G. Disappearance of integrals in systems of more than two degrees of freedom. Celestial Mechanics 17, 167–172 (1978). https://doi.org/10.1007/BF01371328
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/BF01371328