| Differential- algebraic equations is established to solve the dymamic problems of constrained multi-body systems. Numerical method is one way to solve differential-algebraic equations, but some problems arise at the same time as follows: speed and displacement default arising in the process of integration, singular problems of mass matrix, singular problems of constraint equations Jacobian matrix.The aim of this paper is to study new modeling methods and numerical solving strategies to overcome these difficulties. And its main work is as follows:First of all, the paper models the multi-body systems mainly based on gaussian principle of least constraint in generalized coordinates, and it simulate the movement of the system in fractional integral method by finding the extreme value of function with optimization which called genetic algorithms. The new modeling method solves the dymamics problems without establishing differential equations of the systems combined with optimization, and it is much easier and more efficient compared with gaussian principle of least constraint in the form of points.Secondly, the paper study some solving methods to handle with the problems encountered in the process of modeling with explicit form of the equatins of motion presented by Udwadia and Kalaba. The systems may have holonomic and or non-holnomic constraints,which may or may not satisfy D’Alembert’ principle at each instant of time.The equations provide new insights into the behaviour of constrained motion and open up new ways of modelling complex multibody systems.Finally, the paper models the multi-body systems with singular position and singular mass matrix by gaussian principle of least constraint in generalized coordinates and explicit equation. The results show that the two new methods can easily solve the dynamics problemsof multi-body systems with singular position and singular mass matrix. And they can get the acceleration of the system directly without amending the model for one more time. |
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