Abstract: This paper deals with formulation of dynamic equations for multi-rigid-link multi-degree-of-freedom planar mechanical system, holonomic and linear nonholonomic, in arbitrary topological configuration (open-, close- or hybrid-chains). A new dynamic equation with reaction forces and moments of joints which is a simple and unified equation for vectorical and analytical mechanics is presented. These equations are expressed in matrix form. It brings up a dynamical model of overlapping sub-kinematic-chains so that using velocity and accelaration analysis of the system with specifying certain motion inputs, the equivalent dynamic decomposition of the system can be carried out. Amount of computer operations for automatic generation of dynamic equationg briefly depends on kinds of structural units (such as: link-joint, tree-cotree, and singe-opened-chain, etc.) and topological characteristics of a system. After comparing them, the approach by means of order-single-opened chain[18] is better. Esp. It can be carried out directly for untree shaped system without cutting any joint or body.

Key words: 动力学, 机械系统, 拓扑, 1-norm regularization, Incremental echo state network, Kalman filter, model identification, Unmanned surface vehicle