By Victor A. Sadovnichiy, Mikhail Z. Zgurovsky
Focused on contemporary advances, this booklet covers theoretical foundations in addition to numerous purposes. It provides smooth mathematical modeling techniques to the qualitative and numerical research of strategies for advanced engineering difficulties in physics, mechanics, biochemistry, geophysics, biology and climatology. Contributions by means of a world group of revered authors bridge the space among summary mathematical techniques, akin to utilized tools of recent research, algebra, basic and computational mechanics, nonautonomous and stochastic dynamical platforms at the one hand, and sensible functions in nonlinear mechanics, optimization, choice making concept and regulate idea at the different. As such, the publication may be of curiosity to mathematicians and engineers operating on the interface of those fields.
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Extra info for Advances in Dynamical Systems and Control
Fomenko Thus, as a result of the introduction of generalized billiards we have been able not only fully simulate the Euler case, but also to get a large number of systems, whose Fomenko–Zieschang invariants coincide with those calculated previously for many systems of rigid body dynamics. This has allowed to simulate a wide class of problems of rigid body dynamics, though not completely. References 1. : The topology of surfaces of constant energy in integrable Hamiltonian systems, and obstructions to integrability.
18) If λ = 0, then we obtain the classical Goryachev–Chaplygin case. This system is integrable on the zero level of the area integral. The Clebsch case (1871). Motion of a rigid body in a fluid. S12 S2 S2 ε + 2 + 3 + (A1 R12 + A2 R22 + A3 R32 ), 2A1 2A2 2A3 2 ε 1 K = (S12 + S22 + S32 ) − (A2 A3 R12 + A3 A1 R22 + A1 A2 R32 ). V. T. Fomenko The calculation of Fomenko–Zieschang invariants is an effective method for recognizing the Liouville equivalence of the systems. P. A. Oshemkov [15–17]. V. Bolsinov , P.
More precisely, we describe the domains of the invariants of the billiard motion that occur in problems of rigid body dynamics. 2 () Let the domain Θ be that, first, the interior of each elementary domain in its composition does not include points of the focal line, and 2 Billiard Systems as the Models for the Rigid Body Dynamics 27 Fig. 2 In the top row there are domains without conical points at the bottom—with one conical point secondly, any conical point is of the type y (see examples on the Fig.
Advances in Dynamical Systems and Control by Victor A. Sadovnichiy, Mikhail Z. Zgurovsky