Classical Mechanics by H.C. Corben & Philip Stehle

Author:H.C. Corben & Philip Stehle
Language: eng
Format: epub
ISBN: 9780486140780
Publisher: Dover Publications
Published: 2012-10-12T16:00:00+00:00

where ΔJ is the change in J in the time interval Δt. In the limit of infinitesimal , then, the change in J goes to zero even over an extremely long interval of time for which Δa = Δt is finite. The type of external influence considered above, which is sufficiently slow so that the change in energy of the system per period is small compared with the energy itself, and which does not produce resonance, is known as an adiabatic change, and the resulting invariance of J is known as adiabatic invariance.

For a simple harmonic oscillator, we have, from equations (62.7) et seq.,

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