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- W2034199051 abstract "An exact invariant is found for the one dimensional oscillator with equation of motion $ddot q + f( t )dot q + omega ^2 ( t )q = 0$. The method used is that of linear canonical transformations with time-dependent coefficients. These transformations are members of the symplectic group. The Lewis invariant, $I = frac{1}{2}[ rho ^{ - 2} q^2 + ( rho p - dot rho q )^2 ]$ where $ddot rho + omega ^2 ( t )rho = rho ^{ - 3} $, is a particular case of this invariant. The significance of extension to higher dimensions of these results is indicated, in particular for the existence of noninvariance dynamical symmetry groups." @default.
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- W2034199051 date "1978-05-01" @default.
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- W2034199051 title "On a Generalization of the Lewis Invariant for the Time-Dependent Harmonic Oscillator" @default.
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- W2034199051 doi "https://doi.org/10.1137/0134038" @default.
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