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3.7.10 Obtain the extremals (if they exist) of the following problems of Lagrange with functionals, auxiliary conditions and boundary conditions as indicated. Ensure that the problems, as they are stated make sense as problems in the variational calculus. 3.7.10.2 I[x] = int_0^{pi/2} [(dot{x}^2)^2 - (x^2)^2] dt, dot{x}^1 + dot{x}^2 - dot{x}^3 = 0, dot{x}^1 + 2dot{x}^3 = 0, x^1(0) = 0, x^2(0) = 0, x^3(0) = 0, x^1(frac{pi}{2}) = -pi, x^2(frac{pi}{2}) = frac{3pi}{2}, x^3(frac{pi}{2}) = frac{pi}{2}.

          3.7.10 Obtain the extremals (if they exist) of the following problems of Lagrange with functionals, auxiliary conditions and boundary conditions as indicated. Ensure that the problems, as they are stated make sense as problems in the variational calculus.
3.7.10.2
I[x] = int_0^{pi/2} [(dot{x}^2)^2 - (x^2)^2] dt,
dot{x}^1 + dot{x}^2 - dot{x}^3 = 0, dot{x}^1 + 2dot{x}^3 = 0,
x^1(0) = 0, x^2(0) = 0, x^3(0) = 0,
x^1(frac{pi}{2}) = -pi, x^2(frac{pi}{2}) = frac{3pi}{2}, x^3(frac{pi}{2}) = frac{pi}{2}.

$3.7.10 Obtain the extremals (if they exist) of the following problems of Lagrange with functionals, auxiliary conditions and boundary conditions as indicated. Ensure that the problems, as they are stated make sense as problems in the variational calculus. 3.7.10.2 I[x] = int0^pi/2 [(dotx^2)^2 - (x^2)^2] dt, dotx^1 + dotx^2 - dotx^3 = 0, dotx^1 + 2dotx^3 = 0, x^1(0) = 0, x^2(0) = 0, x^3(0) = 0, x^1(fracpi2) = -pi, x^2(fracpi2) = frac3pi2, x^3(fracpi2) = fracpi2.$

Added by Jane L.

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