Discrete and Continuous Models and Applied Computational ScienceDiscrete and Continuous Models and Applied Computational Science2658-46702658-7149Peoples' Friendship University of Russia8606Research ArticleAnalysis of Nonholonomicity Value of Some Hamiltonian FieldsKaspirovichI EDepartment of Theoretical Physics and Mechanicskaspirovich.ivan@mail.ruPopovaV ADepartment of Theoretical Physics and Mechanicsera27525@mail.ruSanyukV IDepartment of Theoretical Physics and Mechanicsvsanyuk@mail.ruPeoples’ Friendship University of Russia150320153546008092016Copyright © 2015,2015In classical mechanics such notion as nonholonomicity is applied only to constraints put on a dynamical system. Besides, Pfaﬃan nonholonomic constraints might be associated with vector ﬁelds. The Nonholonomicity value is one of the principal characteristics of such ﬁelds, which determines properties of geometry of these vector ﬁelds. However, the application of this characteristic in the geometry of vector ﬁelds was restricted only to ﬁelds in Euclidean spaces. Some generalization of nonholonomicity value of vector ﬁelds in non-Euclidean spaces is proposed in this paper. For this purpose the nonholonomicity value is considered as a trilinear form. It is obvious that the coeﬃcients of this form are connected with the components of the metric tensor of the space, where a vector ﬁeld is deﬁned. So generalization of metric tensor on non-Euclidean spaces generates the generalization of the coeﬃcients of trilinear form, which in its turn generates the generalization of nonholonomicity value. As an example, the nonholonomicity values of Hamiltonian vector ﬁelds in sympletic spaces are analyzed in this article. Also it is important to ﬁnd out whether a mechanical interpretation of the received results exists and can we actually apply this method to Hamiltonian ﬁelds.nonholonomicity valuenonholonomic constraintsHamiltonian vector fieldintegrability of differential formsPfaffian formFrobenius theoremстепень неголономностинеголономные связигамильтоново полеинтегрируемость дифференциальных формформа Пфаффаковариант Фробениуса