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IssuesArchive of Issues2016-4pp.501-512

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K.Yu. Osipenko, "Stability of Spatial Motion of a Body with Flow Separation and Rotation about the Symmetry Axis," Mech. Solids. 51 (4), 501-512 (2016)
Year 2016 Volume 51 Number 4 Pages 501-512
DOI 10.3103/S0025654416040129
Title Stability of Spatial Motion of a Body with Flow Separation and Rotation about the Symmetry Axis
Author(s) K.Yu. Osipenko (Ishlinsky Institute for Problems in Mechanics, Russian Academy of Sciences, pr. Vernadskogo 101, str. 1, Moscow, 119526 Russia, kirill-o@mail.ru)
Abstract A model describing the spatial motion (without separation and with nonsymmetric separation of the flow in the medium) of a body rotating about its symmetry axis in a resisting medium is constructed. Several criteria for stability of the body rectilinear motion are obtained in the case of frozen axial velocity. The influence of retardation on the stability of rectilinear motion of a cone is considered.
Keywords penetration, local interaction method, trajectory, flow separation, stability
References
1.  A. I. Bunimovich and A. V. Dubinskii, ""Development, Current State of the Art, and Applications of Local Interaction Theory. Review," Izv. Akad. Nauk. Mekh. Zhidk. Gaza, No. 3, 3-18 (1996) [Fluid. Dyn. (Engl. Transl.) 31 (3), 339-349 (1996)].
2.  R. N. Miroshin and I. A. Khalidov, Local Methods in Continuum Mechanics (Izdat. St. Peterburg Univ., St. Peterburg, 2002) [in Russian].
3.  V. L. Kotov, E. Yu. Linnik, and A. A. Tarasova, "Determination of Parameters of Quadratic Model of Local Interaction as a Spherical Punch Penetrates into a Soft Soil," Probl. Prochn. Plastichn., No. 75(1), 47-55 (2013).
4.  N. A. Ostapenko and G. E. Yakunina, "The Dynamics of Slender Bodies in Dense Media under Conditions of the Local Interaction Model," Prikl. Mat. Mekh. 61 (6), 1008-1033 (1997) [J. Appl. Math. Mech. (Engl. Transl.) 61 (6), 973-985 (1997)].
5.  I. V. Simonov, "The Stability of Motion of an Elongated Rigid Body of Revolution in an Elastoplastic Medium with Flow Separation," Prikl. Mat. Mekh. 64 (2), 313-322 (2000) [J. Appl. Math. Mech. (Engl. Transl.) 64 (2), 299-307 (2000)].
6.  I. V. Simonov, "Classification of Trajectories of the Plane-Parallel Motion of an Axisymmetric Body in a Strong Medium with Flow Separation," Dokl. Ross. Akad. Nauk 386 (2), 198-202 (2002) [Dokl. Phys. (Engl. Transl.) 47 (9), 693-697 (2002)].
7.  K. Yu. Osipenko and I. V. Simonov, "A Model of 3D Dynamics of a Body of Revolution Interacting with Low-Strength Media and Nonsymmetric Cavitation," Izv. Akad. Nauk. Mekh. Tverd. Tela, No. 1, 143-153 (2002) [Mech. Solids (Engl. Transl.) 37 (1), 119-128 (2002)].
8.  I. V. Simonov and K. Yu. Osipenko, "Stability, Paths, and Dynamic Bending of a Blunt Body of Revolution Penetrating into an Elastoplastic Medium," Zh. Prikl. Mekh. Tekhn. Fiz., 45 (3), 146-160 (2004) [J. Appl. Mech. Tech. Phys. (Engl. Transl.) 45 (3), 428-439 (2004)].
9.  K. Yu. Osipenko, "Stability of Spatial Motion of a Body of Revolution in an Elastoplastic Medium," Izv. Akad. Nauk. Mekh. Tverd. Tela, No. 2, 68-77 (2012) [Mech. Solids (Engl. Transl.) 47 (2), 212-220 (2012)].
10.  G. E. Yakunina, "Characteristic Features of the High-Velocity Motion of Bodies in Dense Media," Prikl. Mat. Mekh. 76 (3), 429-449 (2012) [J. Appl. Math. Mech. (Engl. Transl.) 76 (3), 310-323 (2012)].
11.  I. V. Roisman, A. L. Yarin, and M. V. Rubin, "Oblique Penetration of a Rigid Projectile into an Elastic-Plastic Target," Int. J. Impact Engng 19 (9-10), 769-795 (1997).
12.  L. G. Loitsyanskii and A. I. Lur'e, A Course of Theoretical Mechanics, Vol. 2 (Nauka, Moscow, 1983) [in Russian].
13.  V. A. Il'in and E. G. Poznyak, Foundations of Mathematical Analysis, Part 1 (Fizmatlit, Moscow, 2000) [in Russian].
14.  V. I. Kalenova and V. M. Morozov, Nonstationary Linear Systems and Their Applications to Problems of Mechanics (Fizmatlit, Moscow, 2010) [in Russian].
Received 05 March 2014
Link to Fulltext http://link.springer.com/article/10.3103/S0025654416040129
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