Existence And Applications Of Periodic Solutions For 4D Near-hamilton Systems

Research and application of periodic solutions for high-dimensional perturbed near-Hamiltonian systems are important research objects of international dynamics.Nowadays,there are some achievements in this kind of special high-dimensional dynamic system,but many mathematical theories and methods are more abstract,the conditions of theoretical judgment are stronger,and there are still many difficulties in applying them to practical engineering.Therefore,it is necessary to further study the conditions for determining the existence of periodic solutions for high-dimensional perturbed Hamilton systems.In this paper,we study the existence conditions and applications of periodic solutions for 4-dimensional autonomous and non-autonomous near-hamilton systems by analyzing the Poincaré map and Melnikov function.The main contents of this paper are as follows:(1)Study on the existence conditions of periodic solutions for 4D autonomous and non-autonomous near-Hamilton systems.Firstly,the corresponding Poincare map of the system is constructed,and the corresponding Melnikov function is obtained.By analyzing the function,the existence condition of periodic solution of near-hamilton system is obtained.(2)The average system of torsion and respiratory motion systems for large-scale space circular truss antenna torsion with Maple software.And Study the existence of periodic solutions under 1:1 and 2:1 resonance conditions.Firstly,according to the Melnikov function constructed in(1),the Melnikov function of the applied system is obtained.The existence and the upper bound of the periodic solution are studied.The numerical simulation is carried out by means of Matlab software.The obtained results are compared with the phase diagram obtained by numerical simulation.Contrast,thus verifying the correctness of the conclusion.(3)The existence of periodic solution solutions for ring-shaped truss satellite antennas in 2:1 and 1:2 is studied.Similar to(2),the Melnikov function of the non-autonomous system is obtained,and the existence and number of periodic solutions are studied by using the obtained Melnikov function.The upper bound,and numerical simulation using Matlab software.The obtained results are compared with the phase diagram obtained by numerical simulation to verify the correctness of the results.