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4.6.14 Consider the variational problem with Lagrangian function L(x,x) = ² (1 + x)², and boundary conditions x (0) = 0,
Posted: Wed Jul 06, 2022 12:04 pm
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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