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

In particular, when o=0, this yields the definition of a Lyapunov function Finding, for a given supply rate, a valid storage function(or at least proving that one exists)is a major challenge in constructive analysis of nonlinear systems. The most com-

This lecture presents results describing the relation between existence of Lyapunov or storage functions and stability of dynamical systems 6.1 Stability of an equilibria

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

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

在上世纪初,发生了三次概念 上的革命,它们深刻地改变了人们 对物理世界的了解,这就是狭义相 对论(1905)、广义相对论(1916) 和量子力学(1925)

§10–1 动力学的基本定律 §10–2 质点的运动微分方程

EROSPACE DYNAMiCS EXAMPLE: GWE ACCELERATIoN of THE TIP 0F认ERU0毛R人TM5Hc人AF LDk小 G For A650LUT # CCELER升T10 N UTH RES/∈ct T0wE工NERT1 AL FRAME (∈ TH IN THiS CASE) 0EFNE兵8uNcH0 f PoINTS

CoRIoLIS ACcELERAT0 EMYSTIF∈p CONSIOER CASE oF CONSTANT ROTA ToN.No AT0 N OF MME⊙AGUA,ANDc°srAT RADIAL VELOCITY ( As sEEN IN THE RomTIwG 仅AAE

Lecture #4 16.61 Aerospace Dynamics Extension to multiple intermediate frames(two) Copyright 2002 by Jonathan How