The book is written for students of universities and postgraduate students specializing in the field of nonlinear dynamics, as well as specialists in various fields of mechanical engineering. It is devoted to the development of original methods, and outlines the results of analytical studies of dynamical chaos, synchronization, and dynamic structures in lattices of coupled rotators. It presents its findings within the context of the phase space of models and by involving methods of the qualitative theory of differential equations, the theory of bifurcations, and qualitative numerical methods.

Extractable deposits of silver, gold, copper, zinc, lead, gas hydrates and other valuable materials can be found at the ocean floor. The most valuable minerals are found at large depths, starting from 1000 m and deeper. Therefore, the leading offshore companies are currently designing systems and tools for deep sea mining. The mining at the desired depth of a few kilometers is a great challenge though as it has never been attempted before at the commercial scale. One of the fundamental design challenges lays in the understanding of and preventing from the problems associated with the dynamics of a subsea Vertical Transport System (VTS). The function of the VTS is to transport slurry (a thin mixture of water and finely divided minerals) from the seafloor to the mining support vessel. The VTS consists of a vertically hanging submerged pipe through which the slurry is transported upwards and a number of booster stations which maintain the pressure in the pipe that enables the desired slurry flow. The VTS system is subject to a number of the dynamic excitations such as the vessel motion, the slurry flow in the pipe, the sea current and a propulsion device that is envisaged to control the position of the lower end of the pipe at the desired location. To design a reliable VTS system the effect of all the above-mentioned excitation mechanisms has to be accounted for.

This paper studies the conditions for existence and stability of stationary cluster structures in lattices of diffusively coupled dynamical systems within the framework of a new interpretation of cluster synchronization as classical synchronization of cluster oscillators (C-oscillators). The study of existence of cluster attractors is based on the linear chains of cluster oscillators, defining possible types of cluster structures in chains. First, we present interval estimates for the range of coupling strengths in which cluster attractors can exist. Then we formulate and prove the basic theorems about the local stability of the various cluster structures. The presented methodology can be extended to study cluster structures on lattices of different geometry and forms such as linear cluster structures in two-dimensional lattices, layered cluster structures in three-dimensional lattices and cluster structures in ring-shaped systems. Crown

The equivalent dynamic rigidity of the Timoshenko beam resting on an elastoviscous base and interacting with a point object moving uniformly on it is studied. A generic relation for the equivalent rigidity of the beam is obtained and analyzed. The equivalent rigidity is studied as a function of the object velocity. A comparative analysis of equivalent rigidities of the Timoshenko and Bernoulli{Euler beams is performed.