Modern Mathematics and Mechanics Fundamentals, Problems and Challenges - Sadovnichiy, Victor A.; Zgurovsky, Michael Z.; SpringerLink (Online service) (Cham : Springer International Publishing : Imprint: Springer, 2019)
In this book international expert authors provide solutions for modern fundamental problems including the complexity of computing of critical points for set-valued mappings, the behaviour of solutions of ordinary differential equations, partial differential equations and difference equations, or the development of an abstract theory of global attractors for multi-valued impulsive dynamical systems. These abstract mathematical approaches are applied to problem-solving in solid mechanics, hydro- and aerodynamics, optimization, decision making theory and control theory. This volume is therefore relevant to mathematicians as well as engineers working at the interface of these fields.
From the content: Part I Differential Geometry -- Three-dimensional Manifolds of Constant Energy and Invariants of Integrable Hamiltonian Systems -- Convergence Almost Everywhere of Orthorecursive Expansions in Systems of Translates and Dilates -- Topological entropy on non compact sets -- Global Attractors of Multi-valued Impulsive Dynamical Systems: Existence, Invariance and Robustness -- Part II Solid Mechanics -- Procedure of the Galerkin Representation in Transversely Isotropic Elasticity -- Multicomponent Shallow Water System and Two-dimensional ShockWaves -- Asymptotic Behavior of State Functions for Budyko Model with Nonlinear Principal Part on Manifold without Boundary -- Modification Hydrodynamic and Acoustic Fields Generated by a Cavity with Fluid Suction -- Numerical Modeling the Wing Aerodynamics at Angle-of-attack at Low Reynolds Numbers -- Part III Dynamics of Differential and Difference Equations and Applications.
Keywords: Engineering mathematics; System theory; Control theory; Multibody systems; Vibration; Mechanics, Applied; Geometry, Differential; Engineering Mathematics; Systems Theory, Control; Multibody Systems and Mechanical Vibrations; Differential Geometry