Download e-book for iPad: Advances in Dynamical Systems and Control by Victor A. Sadovnichiy, Mikhail Z. Zgurovsky

By Victor A. Sadovnichiy, Mikhail Z. Zgurovsky

ISBN-10: 3319406728

ISBN-13: 9783319406725

ISBN-10: 3319406736

ISBN-13: 9783319406732

Focused on contemporary advances, this e-book covers theoretical foundations in addition to a number of functions. It provides sleek mathematical modeling techniques to the qualitative and numerical research of strategies for complicated engineering difficulties in physics, mechanics, biochemistry, geophysics, biology and climatology. Contributions via a global crew of revered authors bridge the distance among summary mathematical ways, akin to utilized tools of recent research, algebra, primary and computational mechanics, nonautonomous and stochastic dynamical structures at the one hand, and functional functions in nonlinear mechanics, optimization, choice making concept and regulate concept at the different. As such, the ebook could be of curiosity to mathematicians and engineers operating on the interface of those fields.

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29(3), 1–15 (1995) 9. : Integrable Hamiltonian Systems: Geometry, Topology, Classification, 1, 2. Regulyarnaya i Khaolichcskaya Dinamika, Izhevsk (1999). [in Russian] 10. : Methods of calculation of the Fomenko – Ziesehang invariant. In: Topological Classification of Integrable Systems – Advances in Soviet Mathematics, vol 6, 147–183. AMS, Providence (1991) 11. Arkhangelskii, YuA: Analytical Dynamics of a Rigid Body. Nauka, Moscow (1977) 12. : On the motion of a rigid body having cavities filled with homogeneous liquid.

N, N = 1, 2, . . 1) i=1 as t → +∞. Let ·, · Vi : Vi ∗ × Vi → R be the pairing in Vi ∗ × Vi that coincides on H × Vi with the inner product (·, ·) in the Hilbert space H. 1 That is, V i is a real reflexive separable Banach space continuously and densely embedded into a real Hilbert space H, H is identified with its topologically conjugated space H ∗ , Vi∗ is a dual space to Vi . , Gajewski, Gröger, and Zacharias [1, Chap. I]). Z. Zgurovsky National Technical University of Ukraine “Kyiv Polytechnic Institute”, Peremogy Ave.

Billiard motion has the natural integral—the speed |v| of the material point x. If |v| > 0 then we can restrict the system to the isoenergy surface Q3 := {(x, v) ∈ M 4 : |v| = 1}. Such isoenergetic surfaces are homeomorphic to each other and in the subsequent discussion we put |v| = 1. Some restriction of the choice of the boundary allows to find the additional integral. 3 (Jacobi, Chasles [24]) Given a geodesic curve on a quadric in ndimensional Euclidean space, tangent lines which are drawn at arbitrary points on the geodesic are tangent both to this quadric and to n − 2 confocal quadrics, which are the same for all the points on the geodesic.

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Advances in Dynamical Systems and Control by Victor A. Sadovnichiy, Mikhail Z. Zgurovsky

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