... n Note that in the limit case (2.8) and the sign change t -t, the latter system transforms to the EulerPoisson equations for the classical Euler top, M = M в , = в , (2.9) i = ai Mi , ai = ((Jj + Jk - Ji )Ji )-1 , (2.10) which p ossesses first integrals ...
[
Текст
]
Ссылки http://ics.org.ru/upload/iblock/331/161-chaplygin-ball-over-a-fixed-sphere-an-explicit-integration_ru.pdf -- 284.0 Кб -- 28.10.2015 Похожие документы
... Using this and the relations (3.8), on the given level set of the angular momentum integral M = M 0 we find ( xi) = 0 Mx , Ii ... 3.8) and (3.10) completely determine the angular and linear velocities of the ball , V (i) = R в (i) and two possible ...
[
Текст
]
Ссылки http://ics.org.ru/upload/iblock/c34/185-how-to-control-the-chaplygin-ball-using-rotors-ii_en.pdf -- 1774.6 Кб -- 28.10.2015 Похожие документы
... 1 1 1 1 det J ( n , J - 1 n ) 2 k J 2 , = ( n , J - 1 n ) - 2 J- 2 n ; M= k then and the Hamiltonian is the energy integral (8) {Mi , Mj } = - ij k ( 19) The differentials of the integrals (7) and (8), for example, for the solution 3 are determined as Mk ...
[
Текст
]
Ссылки http://ics.org.ru/upload/iblock/400/172-hamiltonization-of-nonholonomic-systems-in-the-neighborhood-of-invariant-manifolds_ru.pdf -- 426.8 Кб -- 28.10.2015 Похожие документы
... energies exist and are equal to m 2 h, T= h. (4) V= m +2 m +2 Here 1 f = lim 0 f (t ... m, then, by Theorem 1, we get the generalized Lagrange identity (3): Ё I0 = 4h0 - 2(m ...
[
Текст
]
Ссылки http://ics.org.ru/upload/iblock/7d3/154-lagrange-s-identity-and-its-generalizations_en.pdf -- 145.8 Кб -- 28.10.2015 Похожие документы
... the three-dimensional vectors M = NJ Obviously, ( , ) = 1, (M , ) = N ( , n) = 0 ... M (22) Introduce the time change ds = G( )dt and fix any level of the energy ... we have F (M ) = 2 M 2 , G( ) = ( , J ) , = det J k2 h and (24) 1 H = M 2 - ( , J ...
[
Текст
]
Ссылки http://ics.org.ru/upload/iblock/e2c/146-rolling-of-a-non-homogeneous-ball-over-a-sphere-without-slipping-and-twisting_ru.pdf -- 190.5 Кб -- 28.10.2015 Похожие документы
... m = dim x is independent of the point x. Consequently, there is a distribution of m ... 2.8) (2.9) It is constant throughout the motion of the sleigh. (2.6) and (2.8) imply ...
[
Текст
]
Ссылки http://ics.org.ru/upload/iblock/c61/166-on-invariant-manifolds-of-nonholonomic-systems_en.pdf -- 240.1 Кб -- 28.10.2015 Похожие документы