4.6.14 Consider the variational problem with Lagrangian function L(x,x) = ² (1 + x)², and boundary conditions x (0) = 0,

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4 6 14 Consider The Variational Problem With Lagrangian Function L X X 1 X And Boundary Conditions X 0 0 1 (56.8 KiB) Viewed 12 times

4.6.14 Consider the variational problem with Lagrangian function L(x,x) = ² (1 + x)², and boundary conditions x (0) = 0, x (1) = m. Show that the extremals are straight lines. Use the condition of Weierstrass to show that (a) if m < -1 or m≥ 0 then the extremal yields a strong minimum. Use the Legendre condition to show the following. (b) If √3 -1<m< then the extremal yields a weak minimum. (c) If 116 then the extremal yields a weak maximum. or 1/2 - 1/³ <m< 6 112 √³ <₁ √3 <m <0