Irregular trajectories in vakonomic mechanical systems
E. R. Avakovab, V. G. Oleinikovab
a Faculty of Mechanics and Mathematics, Moscow State University, Moscow, Russia
b V. A. Trapeznikov Institute of Control Sciences of Russian Academy of Sciences, Moscow
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.
Lagrange principle, abnormal problems, nonintegrable systems, vakonomic dynamics.
PDF file (219 kB)
Computational Mathematics and Mathematical Physics, 2016, 56:10, 1686–1694
E. R. Avakov, V. G. Oleinikov, “Irregular trajectories in vakonomic mechanical systems”, Zh. Vychisl. Mat. Mat. Fiz., 56:10 (2016), 1702–1710; Comput. Math. Math. Phys., 56:10 (2016), 1686–1694
Citation in format AMSBIB
\by E.~R.~Avakov, V.~G.~Oleinikov
\paper Irregular trajectories in vakonomic mechanical systems
\jour Zh. Vychisl. Mat. Mat. Fiz.
\jour Comput. Math. Math. Phys.
Citing articles on Google Scholar:
Related articles on Google Scholar:
|Number of views:|