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A new function, the Hamiltonian, is then defined by H = ∑i q̇i pi − L. From this point it is not difficult to derive and These are called Hamilton's equations.
end{aligned} (9) On the other hand, by [8], Theorem 2, it is not difficult to derive the following.
Employing the method in [16] or [19], it is not difficult to derive that is the solution of problem (3.1).
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