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This book deals with the problem of dynamics of bodies with time-variable mass and moment of inertia. Mass addition and mass separation from the body are treated. Both aspects of mass variation, continual and discontinual, are considered. Dynamic properties of the body are obtained applying principles of classical dynamics and also analytical mechanics. Advantages and disadvantages of both approaches are discussed. Dynamics of constant body is adopted, and the characteristics of the mass variation of the body is included. Special attention is given to the influence of the reactive force and the reactive torque. The vibration of the body with variable mass is presented. One and two degrees of freedom oscillators with variable mass are discussed. Rotors and the Van der Pol oscillator with variable mass are displayed. The chaotic motion of bodies with variable mass is discussed too. To support learning, some solved practical problems are included.

Dynamics. --- Mass (Physics). --- Time. --- Civil & Environmental Engineering --- Engineering & Applied Sciences --- Civil Engineering --- Mass (Physics) --- Hours (Time) --- Gravitational mass --- Inertial mass --- Dynamical systems --- Kinetics --- Geodetic astronomy --- Nautical astronomy --- Horology --- Force and energy --- Gravitation --- Inertia (Mechanics) --- Matter --- Mechanics --- Moments of inertia --- Weight (Physics) --- Mathematics --- Mechanics, Analytic --- Physics --- Statics --- Properties --- Mechanics, applied. --- Mechanics. --- Mathematics. --- Theoretical and Applied Mechanics. --- Classical Mechanics. --- Applications of Mathematics. --- Math --- Science --- Classical mechanics --- Newtonian mechanics --- Dynamics --- Quantum theory --- Applied mechanics --- Engineering, Mechanical --- Engineering mathematics --- Mechanics, Applied. --- Applied mathematics. --- Engineering mathematics. --- Engineering --- Engineering analysis --- Mathematical analysis

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This book provides the presentation of the motion of pure nonlinear oscillatory systems and various solution procedures which give the approximate solutions of the strong nonlinear oscillator equations. The book presents the original author’s method for the analytical solution procedure of the pure nonlinear oscillator system. After an introduction, the physical explanation of the pure nonlinearity and of the pure nonlinear oscillator is given. The analytical solution for free and forced vibrations of the one-degree-of-freedom strong nonlinear system with constant and time variable parameter is considered. Special attention is given to the one and two mass oscillatory systems with two-degrees-of-freedom. The criteria for the deterministic chaos in ideal and non-ideal pure nonlinear oscillators are derived analytically. The method for suppressing chaos is developed. Important problems are discussed in didactic exercises. The book is self-consistent and suitable as a textbook for students and also for professionals and engineers who apply these techniques to the field of nonlinear oscillations.

Physics. --- Mathematical physics. --- Statistical physics. --- Applied mathematics. --- Engineering mathematics. --- Vibration. --- Dynamical systems. --- Dynamics. --- Nonlinear Dynamics. --- Appl.Mathematics/Computational Methods of Engineering. --- Mathematical Applications in the Physical Sciences. --- Mathematical Methods in Physics. --- Vibration, Dynamical Systems, Control. --- Applications of Nonlinear Dynamics and Chaos Theory. --- Mathematical and Computational Engineering. --- Cycles --- Mechanics --- Sound --- Engineering --- Engineering analysis --- Mathematical analysis --- Physical mathematics --- Physics --- Mathematics --- Nonlinear oscillators. --- Chaotic behavior in systems. --- Dynamical systems --- Kinetics --- Mechanics, Analytic --- Force and energy --- Statics --- Natural philosophy --- Philosophy, Natural --- Physical sciences --- Dynamics --- Mathematical statistics --- Statistical methods

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This book deals with the problem of dynamics of bodies with time-variable mass and moment of inertia. Mass addition and mass separation from the body are treated. Both aspects of mass variation, continual and discontinual, are considered. Dynamic properties of the body are obtained applying principles of classical dynamics and also analytical mechanics. Advantages and disadvantages of both approaches are discussed. Dynamics of constant body is adopted, and the characteristics of the mass variation of the body is included. Special attention is given to the influence of the reactive force and the reactive torque. The vibration of the body with variable mass is presented. One and two degrees of freedom oscillators with variable mass are discussed. Rotors and the Van der Pol oscillator with variable mass are displayed. The chaotic motion of bodies with variable mass is discussed too. To support learning, some solved practical problems are included.

Mathematics --- Classical mechanics. Field theory --- Applied physical engineering --- toegepaste wiskunde --- toegepaste mechanica --- economie --- wiskunde --- ingenieurswetenschappen --- mechanica

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In this book the dynamics of the non-ideal oscillatory system, in which the excitation is influenced by the response of the oscillator, is presented. Linear and nonlinear oscillators with one or more degrees of freedom interacting with one or more energy sources are treated. This concerns for example oscillating systems excited by a deformed elastic connection, systems excited by an unbalanced rotating mass, systems of parametrically excited oscillator and an energy source, frictionally self-excited oscillator and an energy source, energy harvesting system, portal frame – non-ideal source system, non-ideal rotor system, planar mechanism – non-ideal source interaction. For the systems the regular and irregular motions are tested. The effect of self-synchronization, chaos and methods for suppressing chaos in non-ideal systems are considered. In the book various types of motion control are suggested. The most important property of the non-ideal system connected with the jump-like transition from a resonant state to a non-resonant one is discussed. The so called ‘Sommerfeld effect’, resonant unstable state and jumping of the system into a new stable state of motion above the resonant region is explained. A mathematical model of the system is solved analytically and numerically. Approximate analytical solving procedures are developed. Besides, simulation of the motion of the non-ideal system is presented. The obtained results are compared with those for the ideal case. A significant difference is evident. The book aims to present the established results and to expand the literature in non-ideal vibrating systems. A further intention of the book is to give predictions of the effects for a system where the interaction between an oscillator and the energy source exist. The book is targeted at engineers and technicians dealing with the problem of source-machine system, but is also written for PhD students and researchers interested in non-linear and non-ideal problems. .

Machinery, Dynamics of --- Data processing. --- Engineering. --- Mathematical physics. --- Applied mathematics. --- Engineering mathematics. --- Continuum mechanics. --- Vibration. --- Dynamical systems. --- Dynamics. --- Continuum Mechanics and Mechanics of Materials. --- Classical Mechanics. --- Appl.Mathematics/Computational Methods of Engineering. --- Statistical Physics and Dynamical Systems. --- Mathematical Applications in the Physical Sciences. --- Vibration, Dynamical Systems, Control. --- Dynamics --- Mechanics. --- Mechanics, Applied. --- Statistical physics. --- Solid Mechanics. --- Mathematical and Computational Engineering. --- Cycles --- Mechanics --- Sound --- Physics --- Mathematical statistics --- Engineering --- Engineering analysis --- Mathematical analysis --- Applied mechanics --- Engineering, Mechanical --- Engineering mathematics --- Classical mechanics --- Newtonian mechanics --- Quantum theory --- Statistical methods --- Mathematics --- Dynamical systems --- Kinetics --- Mechanics, Analytic --- Force and energy --- Statics --- Physical mathematics