Numerical Algorithm For The Constrained Hamilton Equation In Multibody System Dynamics

The development of national defense science and technology puts forward higher requirements for multi-body system dynamics simulation,and it is necessary to design efficient and stable algorithms to meet the simulation requirements.In dynamic simulation of complex mechanical systems,numerical methods with high accuracy and good stability can be designed by keeping the model structure unchanged.In this paper,according to the Hamilton principle and Legendre transformation,we construct the Hamilton equations of multi-body system dynamics with constraints of various indexes.Combined with the trapezoidal formula and the backward second-order difference scheme,we construct the TR-BDF2 method to prove that the method maintains L-stability.Finally,we take the spatial double pendulum as an example to verify the numerical simulation experiment.Then,for each index Constrained Hamiltonian equation,the isometric node,Legendre node and Chebyshev node are selected to construct the single-step block stable and multi-step block stable schemes.The numerical simulation of the double link system and the crank slider system is carried out to verify the schemes.The experimental results of different simulation time,different asynchronous length,different indexes and different nodes are compared,The experimental results show that the method has high accuracy and good stability,and the energy error,displacement and velocity level error can be effectively maintained.In the case of long time simulation,the system energy error can be effectively maintained,but the energy tends to dissipate.Finally,a high-order variational numerical integration method is constructed for the Index-3 Constrained Hamiltonian equation,in which the variables are discretized by Lagrange interpolation method,and the Gauss method is used for numerical integration,so as to improve the accuracy of the algorithm.The results show that the energy can be changed in a bounded range and the displacement constraint can be effectively maintained.Especially,when the simulation time is 1000 s,the energy curve will not shift,which makes up for the lack of energy dissipation of block stability method.