Lie systems and integrability conditions for t-dependent frequency harmonic oscillators

Details Lie systems and integrability conditions for t-dependent frequency harmonic oscillators Lie systems and integrability conditions for t-dependent frequency harmonic oscillators

2009-08-17

arxiv.org/abs/0908.2292v1

International Journal of Geometric Methods in Modern Physics (IJGMMP), Vol. 7, Issue 2, 289-310 (2010)

Physics

Mathematical Physics

Scientific paper

10.1142/S0219887810004014

Time-dependent frequency harmonic oscillators (TDFHO's) are studied through the theory of Lie systems. We show that they are related to a certain kind of equations in the Lie group SL(2,R). Some integrability conditions appear as conditions to be able to transform such equations into simpler ones in a very specific way. As a particular application of our results we find t-dependent constants of the motion for certain one-dimensional TDFHO's. Our approach provides an unifying framework which allows us to apply our developments to all Lie systems associated with equations in SL(2,R) and to generalise our methods to study any Lie system.

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