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The book presents up-to-date and unifying formulations for treating dynamics of different types of mechanical systems with variable mass. The starting point is overview of the continuum mechanics relations of balance and jump for open systems from which extended Lagrange and Hamiltonian formulations are derived. Corresponding approaches are stated at the level of analytical mechanics with emphasis on systems with a position-dependent mass and at the level of structural mechanics. Special emphasis is laid upon axially moving structures like belts and chains and on pipes with an axial flow of fluid. Constitutive relations in the dynamics of systems with variable mass are studied with particular reference to modeling of multi-component mixtures. The dynamics of machines with a variable mass are treated in detail and conservation laws and the stability of motion will be analyzed. Novel finite element formulations for open systems in coupled fluid and structural dynamics are presented.
Designed to be a complete and integrated text on the dynamic properties of machines, mechanisms, and rotors with variable mass, this book presents new results from investigations based on the general dynamics of systems with variable parameters. The book considers both weak and strong nonlinear vibrations of these systems, and chaotic phenomena are also discussed. The conservation laws and adiabatic invariants for systems with variable mass are formulated and the stability and instability conditions of motion are defined.
Arun K. Banerjee is one of the foremost experts in the world on the subject of flexible multibody dynamics. This book describes how to build mathermatical models of multibody systems with elastic components. Examples of such systems include the human body itself, construction cranes, cares with trailers, helicopers, spacecraft deploying antennas, tethered satellites, and underwater maneuvering vehicles. This book provides methods of analysis of complex mechanical systems that can be simulated in less computer time than other methods. It equips the reader with knowledge of algorithms that provide accurate results in reduced simulation time.
Two dramatically different philosophical approaches to classical mechanics were proposed during the 17th - 18th centuries. Newton developed his vectorial formulation that uses time-dependent differential equations of motion to relate vector observables like force and rate of change of momentum. Euler, Lagrange, Hamilton, and Jacobi, developed powerful alternative variational formulations based on the assumption that nature follows the principle of least action. These variational formulations now play a pivotal role in science and engineering.This book introduces variational principles and their application to classical mechanics. The relative merits of the intuitive Newtonian vectorial formulation, and the more powerful variational formulations are compared. Applications to a wide variety of topics illustrate the intellectual beauty, remarkable power, and broad scope provided by use of variational principles in physics.The second edition adds discussion of the use of variational principles applied to the following topics:(1) Systems subject to initial boundary conditions(2) The hierarchy of related formulations based on action, Lagrangian, Hamiltonian, and equations of motion, to systems that involve symmetries.(3) Non-conservative systems.(4) Variable-mass systems.(5) The General Theory of Relativity.Douglas Cline is a Professor of Physics in the Department of Physics and Astronomy, University of Rochester, Rochester, New York.
This comprehensive volume addresses the mechanics of flight through a combination of theory and applications. Topics are presented in a logical order and coverage within each is extensive, including a detailed discussion on the quaterion formulation for six-degree-of-freedom flight.
Designed to be a complete and integrated text on the dynamic properties of machines, mechanisms, and rotors with variable mass, this book presents new results from investigations based on the general dynamics of systems with variable parameters. The book considers both weak and strong nonlinear vibrations of these systems, and chaotic phenomena are also discussed. The conservation laws and adiabatic invariants for systems with variable mass are formulated and the stability and instability conditions of motion are defined.
Rapid developments in nonlinear dynamics and chaos theory have led to publication of many valuable monographs and books. However, most of these texts are devoted to the classical nonlinear dynamics systems, for example the Duffing or van der Pol oscillators, and either neglect or refer only briefly to systems with motion-dependent discontinuities. In engineering practice a good part of problems is discontinuous in nature, due to either deliberate reasons such as the introduction of working clearance, and/or the finite accuracy of the manufacturing processes.The main objective of this volume is to provide a general methodology for describing, solving and analysing discontinuous systems. It is compiled from the dedicated contributions written by experts in the field of applied nonlinear dynamics and chaos.The main focus is on mechanical engineering problems where clearances, piecewise stiffness, intermittent contact, variable friction or other forms of discontinuity occur. Practical applications include vibration absorbers, percussive drilling of hard materials and dynamics of metal cutting.
This book examines the study of mechanical systems as well as its links to other sciences of nature. It presents the fundamentals behind how mechanical theories are constructed and details the solving methodology and mathematical tools used: vectors, tensors and notions of field theory. It also offers continuous and discontinuous phenomena as well as various mechanical magnitudes in a unitary form by means of the theory of distributions.
This book introduces a general approach for schematization of mechanical systems with rigid and deformable bodies. It proposes a systems approach to reproduce the interaction of the mechanical system with different force fields such as those due to the action of fluids or contact forces between bodies, i.e., with forces dependent on the system states, introducing the concepts of the stability of motion. In the first part of the text mechanical systems with one or more degrees of freedom with large motion and subsequently perturbed in the neighborhood of the steady state position are analyzed. Both discrete and continuous systems (modal approach, finite elements) are analyzed. The second part is devoted to the study of mechanical systems subject to force fields, the rotor dynamics, techniques of experimental identification of the parameters and random excitations. The book will be especially valuable for students of engineering courses in Mechanical Systems, Aerospace, Automation and Energy but will also be useful for professionals. The book is made accessible to the widest possible audience by numerous, solved examples and diagrams that apply the principles to real engineering applications.