高阶非完整系统的广义Birkhoff表示

通常方法构造的高阶非完整系统的运动微分方程不仅没有完整系统的辛几何结构和Lie代数结构,而且也不具备完整系统的自伴随性质.本文利用降阶方法,将高阶非完整系统变换为一阶动力学系统,并运用Cauchy-Kowalevski定理对其自伴随化,得到一种新的一阶动力学方程组-广义Birkhoff表示,这将为研究高阶非完整系统的若干动力学问题、几何结构、代数结构、几何数值积分以及工程应用提供了一个新的方法.

Generalized birkhoffian representation of High order nonholonomic systems

The differential equations of motion of high order nonholonomic systems constructed by utilizing the general methods not only lack the symplectic structure and Lie algebra structure of holonomic systems, but also lack the self adjoint nature of holonomic systems. In this paper, the high order nonholonomic system was transformed into first order kinetic system by using the reduced order method, which was self adjointized by making use of the Cauchy Kowalevski theorem, then the generalized Birkhoffian equation of high order nonholonomic system was obtained. This will provide a new method for researching a number of high order nonholonomic system's problems, such as the geometry and algebraic structure, geometric numerical integrator and engineering applications, etc.