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Статья

The Lagrange differential-algebraic equations

Journal of Applied Mathematics and Mechanics. 2014. Vol. 78. No. 6. P. 587-598.
A.A. Burov, Kosenko I. I.

The Lagrange equations are considered in the case when the Lagrangen function is independent of some of the velocities, and the properties of the differential-algebraic equations arising are studied. It is proved that, when non-degeneracy conditions are satisfied, the equations arising reduce to differential Lagrange equations of lower dimension. The problem of the planar oscillations of an elastic pendulum is considered as an example.