Numerical Study Of Complex Dynamical Behavior Of The Two-time Scale System

The characteristic of the rigid-flexible coupling multi-body system isthat there exist both wide range slow variables and slight fast variables.They are coupled to each other, constituting a time-varying, stronglynonlinear and high dimensional kinetic equation. Difficulties are oftenencountered during dynamical simulation process of multi-body system.Studies show that whether the numerical calculation is success or failuresometimes is related with the treatment of the nonlinear terms in the model.In this paper, the idea of qualitative analysis in nonlinear dynamics iscombined with the numerical simulation in multi-body system dynamics,hoping to find a criterion of the correctness and reliability of numericalsimulation by making qualitative analysis of such equations.A two-time scale variable system–the spring pendulum isconstructed. The system is set as the model to study the characteristic ofthe coupling of wide range slow variable and slight fast variable. With theidea of qualitative analysis, the dynamical behaviors of different variablesare studied under the conditions with high frequency ratio, wide rangeinitial swing angle and small initial spring elongation. The correspondingparameter domains are also presented.The numerical solution of dynamical equation demanding higher dueto the existing of coupled fast and slow variables. In this paper, severalcommonly used numerical solutions of ordinary differential equations arecompared in three aspects: conservation of energy, calculation accuracyand calculation efficiency. A more appropriate numerical method to solvesuch nonlinear equation that often exist stiff problems is selected.Referring to the thought of―initial sensitivity‖in nonlinear dynamics, the stability of numerical calculation is studied by analyzing the errorvariation of spring pendulum in the transient time domain. An errordivergence index is proposed to measure the divergence of the error. Thecorrelation between error divergence and system dynamical behavior,control parameter, initial conditions is discussed, and regularityconclusions with universal significance are made.A cubic interpolation precise integration method is introduced. Themethod is a single-step prediction-correction algorithm, capable ofself-starting, and has the characteristics of high precision and small amountof calculation. Conclusion shows that the method is suitable for thetwo-time scale variable system.The results of this paper can be certain reference for the accuracy andreliability of the numerical simulation of rigid-flexible couplingmulti-body system dynamics, and is of great significance to thedevelopment of multi-body system dynamics.