Abstract
We investigate numerically the changes of the adiabatic invariants in some resonant cases of time dependent one-dimensional dynamical systems. We find that at each main resonance of the Mathieu equation there is a “resonant” adiabatic invariant which is much better conserved than other forms of adiabatic invariants. When the orbits are stable the resonant adiabatic invariant does not change appreciably. However, in the case of unstable orbits the variation of this adiabatic invariant becomes progressively larger as the time increases. Then we study the adiabatic invariant in the case of a simple pendulum with varying length. The changes of the adiabatic invariant are of the same order when the motion remains either oscillating or changes from oscillating to rotating.
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© 1982 D. Reidel Publishing Company, Dordrecht, Holland
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Barbanis, B. (1982). The Behaviour of Adiabatic Invariants Near Resonances. In: Mariolopoulos, E.G., Theocaris, P.S., Mavridis, L.N. (eds) Compendium in Astronomy. Springer, Dordrecht. https://doi.org/10.1007/978-94-009-7766-2_4
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DOI: https://doi.org/10.1007/978-94-009-7766-2_4
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