I have showed that if the integrand [tex]f[/tex] in the variational problem(adsbygoogle = window.adsbygoogle || []).push({});

[tex]\delta (\int f dx ) = 0[/tex]

does not depend explicitly on the independent variable x, i.e. satisfies [tex]f = f(y, \dot{y})[/tex], then the Euler equation can be integrated to

[tex]\dot{y} \frac{\partial f}{\partial \dot{y}} - f = const.[/tex]

How can I give an interpretation of this constant for the case that [tex] f = L[/tex] is the Lagrangian and [tex]x = t[/tex] is the time?

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# Interpretation of the Lagrangian

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