Integration of the Euler—Lagrange Equation
Let us suppose that the hypotheses of Theorem 2.3 are met so that the Euler-Lagrange equation (2.22) is of the form (2.23). Let us recall these hypotheses: (i) f(·) is twice continuously differentiable (of class C 2); (ii) f rr [t, x*(t), ẋ*(t)]≠0 for all t ∈[t 0, t 1]; (iii) ẋ*(t) is defined for all t ∈[t 0, t 1].
KeywordsLagrange Equation Continuity Property Admissible Function Average Kinetic Energy Rectilinear Motion
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