[نسايم لليل]

لدي تمرين لم اعرف حله في الميكانيكا التقليدية المتقدمة لمرحلة الماجستير
ارجو مساعدتي
Suppose it is known experimentally that a particle fell a given distance in a time , but the times of fall for distances other than is not known. Suppose further that the Lagrangian for the problem is known, but that instead of solving the equation of motion for as a function of , it is guessed that the functional form is

If the constants and are adjusted always so that the time to fall is correctly given by , show directly that the integral

Is an extremum for real values of the coefficients only when and .