Damped equations of Mathieu type

摘要

We obtain the first integrals of various extensions of the Mathieu equation by exploiting the integrable time-dependent classical dynamics introduced by Bartuccelli and Gentile (2003) [6]. We also compute the Lagrangian of the Van der Pol–Mathieu equation using Jacobi’s last multiplier and consider certain coupled versions of time-dependent equations of the oscillator type.