Analysis And Realization Of Chaotic Dynamics Of Gyro System

The problem of nonlinear vibration generated during the rotation of the gyrostat has always been a difficult problem to be solved,and this problem is extremely important in the aerospace field.During the research of gyrostat systems,many scholars have constructed gyrostat systems with different structures and damping disturbances,and have conducted in-depth research on their nonlinear problems.Most of the existing researches on gyrostat systems use numerical calculations and bifurcation methods to analyze chaotic dynamic characteristics,and rarely analyze the chaotic motion mechanism from the force of the gyrostat system and its corresponding energy.This thesis studies the gyrostat system under different structures and damping disturbances,and analyzes the nonlinear dynamic characteristics of the system from the perspective of force and energy.The main research contents include:(1)A dynamic model of the gyrostat system under disturbance and external torques is constructed,and the force field and corresponding energy conversion of the gyrostat system are studied.Based on the model,the equilibrium point characteristics of the gyrostat system are analyzed.In addition,a kinematic model of this gyrostat system is constructed.The force analysis of the system is performed.By converting the gyrostat system model to the Kolmogorov model,the torque field of the gyrostat system is decomposed into inertial,internal,dissipative,and external torques,and the energy is decomposed into four different energies corresponding to the torques.The mutual conversion between energies is analyzed,and it is found that the dynamic behavior of the system and the formation of the topological structure are closely related to the force and energy conversion of the system.During the research on the internal and external energy conversion of the gyrostat system,Casimir energy is given,and it is revealed that Casimir power is equal to the error power between external power and dissipated power.The mechanism of different dynamic behaviors is analyzed using system state bifurcation,Lyapunov exponent spectrum,Casimir energy bifurcation and error power bifurcation.(2)The problem of hidden chaotic attractors near the stable equilibrium point in a gyrostat system with two stable focal points and a saddle point is studied.The influence of the parameters of the gyrostat system on the characteristics of the equilibrium point is analyzed.Using the equilibrium point stability distribution map and multi-initialvalue bifurcations,it is found that in addition to the self-excited attractor,the stable focal point also has the hidden attractor.Based on the definitions of self-excited and hidden attractors,the essential differences between self-excited chaos and hidden chaos are analyzed through multi-initial-value bifurcation diagrams,multi-initial-value phase diagrams,and the basins of attraction of different attractors.(3)The motion state of the displacement trajectory of the frame gyrostat model is studied by using the finite element analysis method on the COMSOL simulation platform.The finite element analysis and calculation of the gyrostat system are carried out using the COMSOL simulation platform.The displacement simulation results of the finite element analysis method and the numerical calculation method of the kinematic model of the gyrostat system are given and compared and analyzed.The effects of disturbance and external moment on the motion and displacement of the gyrostat system are studied respectively.