Mechanical Systems, Classical Models

Mechanical Systems, Classical Models
Author: Petre P. Teodorescu
Publisher: Springer Science & Business Media
Total Pages: 570
Release: 2008-09-24
Genre: Science
ISBN: 1402089880

As it was already seen in the first volume of the present book, its guideline is precisely the mathematical model of mechanics. The classical models which we refer to are in fact models based on the Newtonian model of mechanics, on its five principles, i. e. : the inertia, the forces action, the action and reaction, the parallelogram and the initial conditions principle, respectively. Other models, e. g. , the model of attraction forces between the particles of a discrete mechanical system, are part of the considered Newtonian model. Kepler’s laws brilliantly verify this model in case of velocities much smaller than the light velocity in vacuum. The non-classical models are relativistic and quantic. Mechanics has as object of study mechanical systems. The first volume of this book dealt with particle dynamics. The present one deals with discrete mechanical systems for particles in a number greater than the unity, as well as with continuous mechanical systems. We put in evidence the difference between these models, as well as the specificity of the corresponding studies; the generality of the proofs and of the corresponding computations yields a common form of the obtained mechanical results for both discrete and continuous systems. We mention the thoroughness by which the dynamics of the rigid solid with a fixed point has been presented. The discrete or continuous mechanical systems can be non-deformable (e. g.

Mechanical Systems, Classical Models

Mechanical Systems, Classical Models
Author: Petre P. Teodorescu
Publisher: Springer Science & Business Media
Total Pages: 778
Release: 2007-06-06
Genre: Science
ISBN: 1402054424

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.

Mechanical Systems

Mechanical Systems
Author: Roger F. Gans
Publisher: Springer
Total Pages: 448
Release: 2014-09-02
Genre: Technology & Engineering
ISBN: 3319083716

This essential textbook concerns analysis and control of engineering mechanisms, which includes almost any apparatus with moving parts used in daily life, from musical instruments to robots. A particular characteristic of this book is that it presents with considerable breadth and rigor both vibrations and controls. Many contemporary texts combine both of these topics in a single, one term course. This text supports the more favorable circumstance where the material is covered in a one year sequence contains enough material for a two semester sequence, but it can also be used in a single semester course combining two topics. “Mechanical Systems: A Unified Approach to Vibrations and Controls” presents a common notation and approach to these closely related areas. Examples from the both vibrations and controls components are integrated throughout this text.

Dynamic Response of Linear Mechanical Systems

Dynamic Response of Linear Mechanical Systems
Author: Jorge Angeles
Publisher: Springer Science & Business Media
Total Pages: 578
Release: 2011-09-15
Genre: Technology & Engineering
ISBN: 1441910263

Dynamic Response of Linear Mechanical Systems: Modeling, Analysis and Simulation can be utilized for a variety of courses, including junior and senior-level vibration and linear mechanical analysis courses. The author connects, by means of a rigorous, yet intuitive approach, the theory of vibration with the more general theory of systems. The book features: A seven-step modeling technique that helps structure the rather unstructured process of mechanical-system modeling A system-theoretic approach to deriving the time response of the linear mathematical models of mechanical systems The modal analysis and the time response of two-degree-of-freedom systems—the first step on the long way to the more elaborate study of multi-degree-of-freedom systems—using the Mohr circle Simple, yet powerful simulation algorithms that exploit the linearity of the system for both single- and multi-degree-of-freedom systems Examples and exercises that rely on modern computational toolboxes for both numerical and symbolic computations as well as a Solutions Manual for instructors, with complete solutions of a sample of end-of-chapter exercises Chapters 3 and 7, on simulation, include in each “Exercises” section a set of miniprojects that require code-writing to implement the algorithms developed in these chapters

Geometric Control of Mechanical Systems

Geometric Control of Mechanical Systems
Author: Francesco Bullo
Publisher: Springer
Total Pages: 727
Release: 2019-06-12
Genre: Science
ISBN: 1489972765

The area of analysis and control of mechanical systems using differential geometry is flourishing. This book collects many results over the last decade and provides a comprehensive introduction to the area.

Stability and Convergence of Mechanical Systems with Unilateral Constraints

Stability and Convergence of Mechanical Systems with Unilateral Constraints
Author: Remco I. Leine
Publisher: Springer Science & Business Media
Total Pages: 241
Release: 2007-12-29
Genre: Technology & Engineering
ISBN: 3540769757

While the stability theory for systems with bilateral constraints is a well-established field, this monograph represents a systematic study of mechanical systems with unilateral constraints, such as unilateral contact, impact and friction. Such unilateral constraints give rise to non-smooth dynamical models for which stability theory is developed in this work. The book will be of interest to those working in the field of non-smooth mechanics and dynamics.

Mathematical Methods of Classical Mechanics

Mathematical Methods of Classical Mechanics
Author: V.I. Arnol'd
Publisher: Springer Science & Business Media
Total Pages: 530
Release: 2013-04-09
Genre: Mathematics
ISBN: 1475720637

This book constructs the mathematical apparatus of classical mechanics from the beginning, examining basic problems in dynamics like the theory of oscillations and the Hamiltonian formalism. The author emphasizes geometrical considerations and includes phase spaces and flows, vector fields, and Lie groups. Discussion includes qualitative methods of the theory of dynamical systems and of asymptotic methods like averaging and adiabatic invariance.

Classical Systems in Quantum Mechanics

Classical Systems in Quantum Mechanics
Author: Pavel Bóna
Publisher: Springer Nature
Total Pages: 243
Release: 2020-06-23
Genre: Science
ISBN: 3030450708

This book investigates two possibilities for describing classical-mechanical physical systems along with their Hamiltonian dynamics in the framework of quantum mechanics.The first possibility consists in exploiting the geometrical properties of the set of quantum pure states of "microsystems" and of the Lie groups characterizing the specific classical system. The second approach is to consider quantal systems of a large number of interacting subsystems – i.e. macrosystems, so as to study the quantum mechanics of an infinite number of degrees of freedom and to look for the behaviour of their collective variables. The final chapter contains some solvable models of “quantum measurement" describing dynamical transitions from "microsystems" to "macrosystems".

Statistical Mechanics of Lattice Systems

Statistical Mechanics of Lattice Systems
Author: Sacha Friedli
Publisher: Cambridge University Press
Total Pages: 643
Release: 2017-11-23
Genre: Mathematics
ISBN: 1107184827

A self-contained, mathematical introduction to the driving ideas in equilibrium statistical mechanics, studying important models in detail.

Nonholonomic Motion of Rigid Mechanical Systems from a DAE Viewpoint

Nonholonomic Motion of Rigid Mechanical Systems from a DAE Viewpoint
Author: Patrick J. Rabier
Publisher: SIAM
Total Pages: 143
Release: 2000-01-01
Genre: Mathematics
ISBN: 089871446X

Focuses on rigid body systems subjected to kinematic constraints and discusses in detail how the equations of motion are developed. The authors show that such motions can be modeled in terms of differential algebraic equations (DAEs), provided only that the correct variables are introduced.