On a Change of Variables in Lagrange’s EquationsстатьяИсследовательская статья
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Аннотация:This paper studies a material system with a finite number of degrees of freedom the motion ofwhich is described by differential Lagrange’s equations of the second kind. A twice continuouslydifferentiable change of generalized coordinates and time is considered. It is well known that theequations of motion are covariant under such transformations. The conventional proof of thiscovariance property is usually based on the integral variational principle due to Hamilton andOstrogradskii. This paper gives a proof of covariance that differs from the generally acceptedone. In addition, some methodical examples interesting in theory and applications are considered.In some of them (the equilibrium of a polytropic gas sphere between whose particles the forcesof gravitational attraction act and the problem of the planar motion of a charged particle in thedipole force field) Lagrange’s equations are not only covariant, but also possess the invarianceproperty.