18
where the time constants are
T^L = Cτn∕∂Li ^^Na — Cm∣ C)Na, and 7⅛ — Cm∕ Qκ∙
Representing the quasi-active system as a linear system permits both an analytic solu-
tion via the eigenvalue decomposition and also a description of the resonant behavior
of (2.3) in terms of the eigenvalues of A.
Recall that the linear system given in (2.12) has the analytic solution
z{t) = eAt ( [ e~AsBu(s)ds + z(0)^ . (2∙14)
Vo /
Assuming A is diagonalizable, it has an eigenvalue decomposition
A = RAIZ-1, (2.15)
where A is a diagonal matrix. That is, the jth column of V is the eigenvector corre-
|
Sponding to the eigenvalue A7 = z(t) = VeAt n =Σ'∙ J=I |
= Λj∙j∙. Then substituting (2.15) into (2.14) yields ( /" e~Ascu(s)ds + z(0)^ Vo / r∙je^t f [ e~λjsCju(s)ds + ¾(0)λj , |
where c = V λB, which is a vector in this example system. The integral can be
More intriguing information
1. CROSS-COMMODITY PERSPECTIVE ON CONTRACTING: EVIDENCE FROM MISSISSIPPI2. The Role of Immigration in Sustaining the Social Security System: A Political Economy Approach
3. A parametric approach to the estimation of cointegration vectors in panel data
4. Gender stereotyping and wage discrimination among Italian graduates
5. Life is an Adventure! An agent-based reconciliation of narrative and scientific worldviews
6. The name is absent
7. The technological mediation of mathematics and its learning
8. On the Relation between Robust and Bayesian Decision Making
9. Modelling Transport in an Interregional General Equilibrium Model with Externalities
10. The name is absent