事件空间中完整力学系统的梯度表示

A gradient representation of holonomic system in the event space

本文研究事件空间中完整力学系统的梯度表示和分数维梯度表示,建立系统的微分方程并将其表示为一阶形式,给出系统成为梯度系统的条件以及成为分数维梯度系统的条件.最后,举例说明结果的应用.

The dynamics research in the event space has important geometric and mechanical meanings,and great progress has been made in this field.A gradient system is a kind of important systems in differential equations and dynamical systems,and is receiving more and more attention.In this paper,a gradient representation and a fractional gradient representation of a holonomic system in the event space are studied.First,the differential equations of motion for the system are established and expressed in the first order form.Second,we have obtained the condition under which the system can be considered as a gradient system and also the condition under which the system can be considered as a fractional gradient system.When a constrained mechanical system is transformed into a gradient system or a fractional gradient system,one can use the properties of the gradient system or the fractional gradient system to study the integration and the stability of a constrained mechanical system.Finally,two examples are given to illustrate the application of the results.The event space is known as more extensive than the configuration space,therefore,the result in the configuration space is a special case of this paper.