Irregular trajectories in vakonomic mechanical systems

E. R. Avakov^ab, V. G. Oleinikov<sup>ab

a</sup> Faculty of Mechanics and Mathematics, Moscow State University, Moscow, Russia
^b V. A. Trapeznikov Institute of Control Sciences of Russian Academy of Sciences, Moscow

Abstract: In his works, V.V. Kozlov proposed a mathematical model for the dynamics of a mechanical system with nonintegrable constraints, which was called vakonomic. In contrast to the then conventional nonholonomic model, trajectories in the vakonomic model satisfy necessary conditions for a minimum in a variational problem with equality constraints. We consider the so-called irregular case of this variational problem, which was not covered by Kozlov, when the trajectory is a singular point of the constraints and the necessary minimum conditions based on the Lagrange principle make no sense. This situation is studied using the theory of abnormal problems developed by the first author. As a result, the classical necessary minimum conditions are strengthened and developed to this class of problems.

Key words: Lagrange principle, abnormal problems, nonintegrable systems, vakonomic dynamics.

UDC: 519.642.8

Received: 01.01.2015

DOI: 10.7868/S0044466916100021

 English version: Computational Mathematics and Mathematical Physics, 2016, 56:10, 1686–1694

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