2025/04/30 by Yagasaki, Kazuyuki
#34C37 #34D10 #37C29 #37J30 #70E20 #70K44 #Dynamical Systems (math.DS) #FOS: Mathematics
paper · doi:10.48550/arxiv.2505.00088
We consider time-periodic perturbations of analytically integrable systems in the sense of Bogoyavlenskij and study their real-meromorphic nonintegrability, using a generalized version due to Ayoul and Zung of the Morales-Ramis theory. The perturbation terms are assumed to have finite Fourier series in time, and the perturbed systems are rewritten as higher-dimensional autonomous systems having the small parameter as a state variable. We show that if the Melnikov functions are not constant, then the autonomous systems are not real-meromorphically integrable near homo- and heteroclinic orbits. We illustrate the theory for rotational motions of a periodically forced rigid body, which provides a mathematical model of a quadrotor helicopter.