 | | Mechanics of Solids
A Journal of Russian Academy of Sciences | | Founded
in January 1966
Issued 6 times a year
Print ISSN 0025-6544
Online ISSN 1934-7936 |
Archive of Issues
| Total articles in the database: | | 12854 |
| In Russian (Èçâ. ÐÀÍ. ÌÒÒ): | | 8044
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| In English (Mech. Solids): | | 4810 |
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| V.Yu. Ol'shanskii, "Construction of Linear Invariant Relations of Kirchhoff Equations," Mech. Solids. 54 (1), 70-80 (2019) |
| Year |
2019 |
Volume |
54 |
Number |
1 |
Pages |
70-80 |
| DOI |
10.3103/S0025654419010060 |
| Title |
Construction of Linear Invariant Relations of Kirchhoff Equations |
| Author(s) |
V.Yu. Ol'shanskii (Institute of Precision Mechanics and Control Problems of the Russian Academy of Sciences, ul. Rabochaya 24, Saratov, 410028 Russia, olshanskiy_vlad@mail.ru) |
| Abstract |
For the Kirchhoff equations in the general case, when the cross-term matrix of the Hamiltonian can be asymmetric, the existence conditions for a linear invariant relation of a general form that connect the impulsive moment and the impulsive force are obtained. It is shown that equations with such an invariant relation can be transformed into the equations with an invariant relation for an impulsive moment, the existence conditions of which with a symmetric cross-term matrix coincide with the Chaplygin case. A description of a set of Hamiltonians that admit the existence of a linear invariant relation of a general form is given. The coordinate form of the invariant relation and its existence conditions is obtained. The total number of conditions is six (in contrast to the eight conditions in the Chaplygin case). Reduction to the Riccati equation is preformed. It is shown that if there is a linear integral, then the Kirchhoff equations are reduced to the Kirchhoff case. |
| Keywords |
Kirchhoff equations, asymmetric cross-term matrix of the Hamiltonian, linear invariant relation |
| Received |
22 June 2017 |
| Link to Fulltext |
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