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IssuesArchive of Issues2002-6pp.29-33

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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
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