 | | 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: | | 11223 |
| In Russian (Èçâ. ÐÀÍ. ÌÒÒ): | | 8011
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| In English (Mech. Solids): | | 3212 |
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| M. U. Nikabadze, "Generalizations of the Huygens-Steiner theorem and Bour formula and some their applications," Mech. Solids. 39 (3), 49-57 (2004) |
| Year |
2004 |
Volume |
39 |
Number |
3 |
Pages |
49-57 |
| Title |
Generalizations of the Huygens-Steiner theorem and Bour formula and some their applications |
| Author(s) |
M. U. Nikabadze (Moscow) |
| Abstract |
The moment of inertia with respect to an axis, tensor of inertia with respect to a point, product of inertia with respect to intersecting axes, and, in particular, axial moments of inertia and products of inertia with respect to the coordinate axes and the moment of inertia with respect to a point (polar moment of inertia) are defined.
The relationship between two tensors of inertia considered with respect to two different poles is established. On the basis of this relationship, the generalized Huygens-Steiner theorem is stated and proved, from which, in turn, the classical theorem is obtained. Several propositions for the moments of inertia are presented.
The classical Bour formula is written and generalized to the cases of the second and nth (n>2) rank tensors. For a tensor of rank n≥2, the definition of the transposed kth order tensor is given. Some propositions concerning this definition and implications of them are stated.
The expressions for the angular momentum and kinetic energy are presented both for a system of material particles in compound motion and for a free rigid body, in particular, for a rigid body rotating about a fixed point. For the last cases, the angular momentum and kinetic energy are expressed in several forms.
On the basis of the generalized Bour formula, the dynamic Euler equations are given in the vector form. |
| References |
| 1. | P. Appel, Theoretical Mechanics [Russian translation], Gostekhizdat,
Moscow, 1960. |
| 2. | N. V. Butenin, Ya. L. Lunts, and D. R. Merkin, Course in Theoretical Mechanics [in Russian], Lan, St. Petersburg, 1998. |
| 3. | N. N. Buhgolts, Basic Course in Theoretical Mechanics [in Russian],
Nauka, Moscow, 1972. |
| 4. | V. G. Vil'ke, Theoretical Mechanics. Textbook [in Russian], Izd-vo MGU,
Moscow, 1998. |
| 5. | A. I. Lur'e, Nonlinear Theory of Elasticity [in Russian], Nauka,
Moscow, 1980. |
| 6. | B. E. Pobedrya, Lectures on Tensor Analysis [in Russian], Izd-vo MGU,
Moscow, 1986. |
|
| Received |
09 November 2001 |
| << Previous article | Volume 39, Issue 3 / 2004 | Next article >> |
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