Lyapunov analysis, which uses monotonicity of a given function of system state along trajectories of a given dynamical system, is a major tool of nonlinear system analysis It is possible, however, to use monotonicity of volumes of subsets of the state space to predict certain properties of system behavior. This lecture gives an introduction to suc methods

where f:R\×Rn×R→ R\ and g:R\×R\×R→ R are continuous functions. Assume that f, g are continuously differentiable with respect to their first two arguments in a neigborhood of the trajectory co(t), yo(t), and that the derivative

3.1.2 A general uniqueness theorem The key issue for uniqueness of solutions turns out to be the maximal slope of a=a(a) to guarantee uniqueness on time interval T=[to, t,, it is sufficient to require existence of a constant M such that

with x(0)=I exist and are unique on the time interval t E [ 0, 1] for allTER\.Then discrete time system(4. 1)with f(5)=r(, i)describes the evolution of continuous time system(4.)at discrete time samples. In particular, if a is continuous then so is f Let us call a point in the closure of X locally attractive for system(4. 1)if there exists

Definition A real-valued function V: X H R defined on state space X of a system with behavior set B and state r:B×[0,∞)→ X is called a Lyapunov function if tHv(t)=v(a(t))=v(a(z(), t)) is a non-increasing function of time for every z E B according to this definition, Lyapunov

he variable t is usually referred to as the\time Note the use of an integral form in the formal definition(2.2): it assumes that the function tHa(a(t), t)is integrable on T, but does not require =a(t)to be differentiable at any particular point, which turns out to be convenient for working with discontinuous

1·飞行力学学科的定义 飞行力学学科的定义有不同的说法,最一般的说法是飞行力 学是研究飞行器运动规律的学科,是应用力学的一个新分支。它 是按照力学的基本原理结合具体对象一—飞行器来分析、研究在 有控制或无控制情况下飞行器运动特性的一门学科

根据生命科学的研究对象进行分类,动力学的理论方法在不同尺度生物系统上的应用做了回顾与总结,重点阐述了近年来的相关研究进展

简要分析了等离子体磁流体发电系统的工作原理和发电过程,阐述了目前磁流体发电研究中的重点和关键问题,从数值模拟和实验研究两方面回顾了国内外的研究情况和研究进展。分析认为等离子体磁流体动力学将会受到越来越多的重视,且将会推动航空航天技术的进步

LECTURE+ 12 RIGID BODY OYNAAICS 工 MPLICAT IONsF GENERAL ROTATIONAL OYWMICS EJLER's EQUATIN of MOTION TORQVE FREE SPECIAL CASES. PRIMARY LESSONS: 30 ROTATONAL MOTION MUCH MORE COMPLEX THAN PLANAR (20) EULER'S E.o.M. PROVIOE STARTING POINT FoR ALL+ OYwAmIcs SOLUTINS To EvlER's EQuATIONS ARE COMPLEX BUT WE CAN OEVE LOP GooO GEOMETRIC VISUALIZATION TOOLS