FlexibleElectronics with NanoManufacturing

This blog is a review on computational method in multibody dynamics. The main topics are geometric algorithm, which is established based on Hamilton principle. It's well known to us that the geometric integration method of the dynamical system is an attractive direction in the last two decades. Dynamic equations of multibody systems, such as differential equation, differential-algebraic equation, are a kind of representative dynamical systems.

The significance of the transformation from Lagrange framework to Hamilton framework is the configuration transformation from Euclidian to Hamiltonian. Then, the symplectic variable is introduced into the mechanics system, and the symplectic integration method can be adopted to solve the dynamic equations. It is able to predict the qualitative information of the multibody dynamic system which is expected to be kept in the process of discretization. It should be specially emphasized when these qualitative information denotes some pivotal physics meaning. How to establish the Hamiltonian canonical equations of the multibody system (multi-rigid body system without constraint or with holonomic constraint, flexible multibody system) is simply described, and how to build the geometric integral method is emphasized in this paper, especially computational geometric mechanics method with promising application, including high-order symplectic algorithm(synthesized algorithm, Partition-synthesized algorithm, symplectic precise integration algorithm), multi-symplectic algorithm and Lie group algorithm(projected method and located coordination method).

力学进展: http://www.cstam.org.cn/lxjz/qikan/Cpaper/zhaiyao.asp?bsid=2006782