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9 Variational Principles in Mechanics and Their Applications
9.20 Find the Hamiltonian form of Euler equations of the functional J =
x 1
x 0
x yy
2 dx.
9.21 Find the Hamiltonian form of Euler equations of the functional J =
x 1
x 0
x 2 + y 2
1 + y 2 dx.
9.22 Find the Hamiltonian form of Euler equations of the functional J =
π
0 (y
2
1 + y
2
2 + y
2
2 )dx.
9.23 Find the Hamiltonian form of Euler equations of the functional J =
x 2
x 0
(x
2
+ y 1 y
2
1 + y 2 y
2
2 )dx.
9.24 Find the Hamiltonian form of Euler equations of the functional J =
x 1
x 0
2x y 1 − y
2
1 +
y
3
2
3
dx.