Fal!2001 16.3122-4 How proceed? 1. For the 2n system (t) A Burau B 入(t) CTR,C 入(t) define a transition matrix Fil(t1, to) F12t1, to F(t1, to) F21t1, to) F22t1,to and use this to relate a(t)to a (t) and X(tf) F1(,tF2(4+)1[x(t) A(」F21(t)h2(,t)A(t SO (t)=F1(t,tx(t)+F12(t,t+)入(t) Fu(t,ty)+ Fi2(t, t)Pira(tf) 2. Now find X(t) in terms of a(tf) ()=|F2(t,t)+Ft,t)P|a(+) 3. Eliminate a(tf)to get N(t)=F2(t,t)+F2(t,tP-F1(t+)+F12(t+)Pa2( P(t)x(tFall 2001 16.31 22—4 • How proceed? 1. For the 2n system " # ∙ ∙ x˙(t) A −BuR−1 uu Bu T x(t) λ˙(t) ¸ = −Cz TRzzCz −AT λ(t) ¸ define a transition matrix " # F11(t1, t0) F12(t1, t0) F(t1, t0) = F21(t1, t0) F22(t1, t0) and use this to relate x(t) to x(tf ) and λ(tf ) " # ∙ ∙ λ(t) ¸ = x(t) F11(t,tf ) F12(t,tf ) x(tf ) F21(t,tf ) F22(t,tf ) λ(tf ) ¸ so x(t) = F h 11(t,tf )x(tf ) + F12(t,tf ) i λ(tf ) = F11(t,tf ) + F12(t,tf )Ptf x(tf ) 2. Now find λ(t) in terms of x(tf ) h i λ(t) = F12(t,tf ) + F22(t,tf )Ptf x(tf ) 3. Eliminate x(tf ) to get: h i h i−1 λ(t) = F12(t,tf ) + F22(t,tf )Ptf F11(t,tf ) + F12(t,tf )Ptf x(t) , P(t)x(t)