16.61 Aerospace Dynamics Spring 2003 Derivation of lagrangian equations Basic Concept: Virtual Work Consider system of N particles located at(, x2, x,,.x3N )with 3 forces per particle(f. f, f..fn). each in the positive
Ch. 24 Johansen's mle for Cointegration We have so far considered only single-equation estimation and testing for cointe- gration. While the estimation of single equation is convenient and often consis- tent, for some purpose only estimation of a system provides sufficient information This is true, for example, when we consider the estimation of multiple cointe- grating vectors, and inference about the number of such vectors. This chapter examines methods of finding the cointegrating rank and derive the asymptotic
12.1 Systems with controllable linearizations A relatively straightforward case of local controllability analysis is defined by systems with controllable linearizations 12.1.1 Controllability of linearized system Let To: 0, THR, uo: 0, T]H Rm be a
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