 | | 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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| A. V. Krutov, "Geometrical model of motion of a rigid body with a fixed point based on a classification of curves," Mech. Solids. 37 (6), 29-33 (2002) |
| Year |
2002 |
Volume |
37 |
Number |
6 |
Pages |
29-33 |
| Title |
Geometrical model of motion of a rigid body with a fixed point based on a classification of curves |
| Author(s) |
A. V. Krutov (Voronezh) |
| Abstract |
An interpretation of the Gauss-Bonnet theorem
of classical differential geometry is given on the basis of geometric
and kinematic representations of the motion
of a rigid body with a fixed point [1] and a geometric-kinematic
classification of curves according to their complexity [2].
Attention to the problem of such an interpretation was drawn in [3].
The potentials of this theorem to be utilized in theoretical
mechanics are revealed. In particular, the problem
of the determination of the angle of rotation of a rigid body
is treated from the geometry standpoint. Various statements and solutions
of this problem, based on a different approach,
have been given in [1, 3]. |
| References |
| 1. | V. Ph. Zhuravlev, Fundamentals of Theoretical Mechanics
[in Russian], Nauka, Moscow, 1997. |
| 2. | A. V. Krutov, "Classification and equations of curves,"
Vestnik VGU. Ser. 2. Estestvennye Nauki, No. 2, pp. 210-217, 1996. |
| 3. | V. Ph. Zhuravlev, "Solid angle theorem in dynamics
of a rigid body," PMM [Applied Mathematics and Mechanics],
Vol. 60, No. 2, pp. 323-326, 1996. |
| 4. | A. V. Krutov, "Some concepts and relations in kinematical
geometry," Beitrage zur Algebra und Geometrie, Bd. 31, S. 87-102, 1990. |
| 5. | A. V. Krutov, "A sequence of bases of a curve and its applications:
Geometric-kinematic model," in Mathematical Modeling of Information
and Technological Systems: Collected Works of Voronezh State Technological
Academy [in Russian], No. 4, pp. 31-38, Voronezh. Gos. Tekh. Akademiya,
Voronezh, 2000. |
| 6. | A. P. Norden, A Short Course in Differential Geometry
[Russian translation], Fizmatgiz, Moscow, 1958. |
| 7. | D. J. Struik, Lectures on Classical Differential Geometry,
Dover, New York, 1988. |
| 8. | V. I. Krutov, Automatic Regulation and Control of Internal
Combustion Engines [in Russian], Mashinostroenie, Moscow, 1989. |
| 9. | V. I. Krutov, Electronic Systems of Regulation and Control
of Internal Combustion Engines, Izd-vo MGTU, Moscow, 1991. |
|
| Received |
18 June 2001 |
| << Previous article | Volume 37, Issue 6 / 2002 | Next article >> |
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