Adiabatic Invariants and the “Third” Integral
- 1 May 1966
- journal article
- research article
- Published by AIP Publishing in Journal of Mathematical Physics
- Vol. 7 (5), 788-797
- https://doi.org/10.1063/1.1931208
Abstract
In a general case of Hamiltonian systems of n degrees of freedom, depending periodically on time, n formal “third” integrals of motion are found. Their application in finding boundaries for the orbits is illustrated in a special case. Then a comparison is made between these integrals and the adiabatic invariants. Both are series expansions but the small parameter used is of different character in each case. This is shown explicitly in a simple example and the relative accuracy of the two expansions is discussed.Keywords
This publication has 7 references indexed in Scilit:
- Resonance cases and small divisors in a third integral of motion. IThe Astronomical Journal, 1963
- A Classification of the Integrals of Motion.The Astrophysical Journal, 1963
- On the existence of a third integral of motionThe Astronomical Journal, 1963
- Asymptotic Theory of Hamiltonian and other Systems with all Solutions Nearly PeriodicJournal of Mathematical Physics, 1962
- The nonconstancy of the adiabatic invariantsAnnals of Physics, 1961
- Adiabatic Invariants of Periodic Classical SystemsPhysical Review B, 1959
- Problème général de la stabilité du mouvementAnnales de la faculté des sciences de Toulouse Mathématiques, 1907