T - IfB

Lagrange multipliersObtain λ 12 and λ 23 by inserting theseexpressions into the constraint condition:x t tx t t dx t tx t t d2 21( ) 2( ) 122 22( ) 3( ) 2343Lagrange multipliersThis gives the following coupled quadratic eqs.: 1 1 x ( tt) x ( tt) t r ( t) t r ( t)d ! ! 2 2 2321 2 12 12 23 12m1 m2 m2 1 1 x ( tt) x ( tt) t r ( t) t r ( t)d ! ! 2 2 1222 3 23 23 12 23m2 m3 m2Solve them to get λ 12 and λ 23 then usethese λ 12 and λ 23 to calculate .x ( t+ Δt)i2244