Continuum Of Motion Equations And Control Laws For Underactuated Mechanical Systems
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| Author | : Constance Ann Lare |
| Publisher | : |
| Total Pages | : |
| Release | : 2021 |
| Genre | : |
| ISBN | : |
As sizes, lengths, or shapes of a system grow large or shrink to zero, a system will approach limiting forms. As the parameter is allowed to grow or shrink, the system could resemble a simpler system. The sufficient conditions for when the equations of motion will morph from the original system to a target system will be presented. The ball and arc equations of motion morph to those of the ball and beam as the arc's radius is allowed to grow. The equations of motion for the rotary pendulum, pendubot, and two-link robot manipulator will morph to the equations of motion of the inverted pendulum cart. The effect of a parameter growing large or shrinking to zero has on the controller for the original system will not be fully investigate in this work. A case for when controller morphing might be possible will be examined. A controller for the rotary pendulum will morph to a controller that stabilizes the inverted pendulum cart. Next, a controller for the pendubot will be morphed that does not stabilize the dimensionless inverted pendulum cart. Lastly, a controller for a fully actuated two-link robot manipulator will be morphed to a stabilizing controller for a fully actuated inverted pendulum cart.
| Author | : W. Michael Lai |
| Publisher | : Gulf Professional Publishing |
| Total Pages | : 580 |
| Release | : 1996 |
| Genre | : Science |
| ISBN | : 9780750628945 |
Continuum mechanics studies the response of materials to different loading conditions. The concept of tensors is introduced through the idea of linear transformation, and the interrelation of direct notation, indicial notation, and matrix operations is also presented. A wide range of idealized materials are considered through simple static and dynamic problems.
| Author | : Margarita E. Eglit |
| Publisher | : World Scientific |
| Total Pages | : 286 |
| Release | : 1996 |
| Genre | : Continuum mechanics |
| ISBN | : 9789810229627 |
| Author | : C. S. Jog |
| Publisher | : CRC Press |
| Total Pages | : 280 |
| Release | : 2002 |
| Genre | : Continuum mechanics |
| ISBN | : 9780849324147 |
| Author | : Zdeněk Martinec |
| Publisher | : Springer |
| Total Pages | : 256 |
| Release | : 2019-05-31 |
| Genre | : Mathematics |
| ISBN | : 3030053903 |
This book addresses the basic concepts of continuum mechanics, that is, the classical field theory of deformable bodies. The theory is systematically developed, from the kinematics to the balance equations, the material theory, and the entropy principles. In turn, the linear-elastic solids, the ideal liquid and the Newtonian liquid are presented in detail as concrete applications. The book concludes by covering the theory of small motions in a medium with a finite prestress. In general, the emphasis is on presenting the content in a clear and straightforward way that requires only an elementary grasp of calculus, linear algebra, and Newtonian mechanics. The book is intended for students of physics, mechanics, engineering and the geosciences, as well as applied mathematics, with a year or more of college calculus behind them.
| Author | : S.K. Godunov |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 263 |
| Release | : 2013-03-09 |
| Genre | : Computers |
| ISBN | : 1475751176 |
Elements of Continuum Mechanics and Conservation Laws presents a systematization of different models in mathematical physics, a study of the structure of conservation laws, thermodynamical identities, and connection with criteria for well-posedness of the corresponding mathematical problems. The theory presented in this book stems from research carried out by the authors concerning the formulations of differential equations describing explosive deformations of metals. In such processes, elasticity equations are used in some zones, whereas hydrodynamics equations are stated in other zones. Plastic deformations appear in transition zones, which leads to residual stresses. The suggested model contains some relaxation terms which simulate these plastic deformations. Certain laws of thermodynamics are used in order to describe and study differential equations simulating the physical processes. This leads to the special formulation of differential equations using generalized thermodynamical potentials.
| Author | : Margarita E Eglit |
| Publisher | : World Scientific Publishing Company |
| Total Pages | : 553 |
| Release | : 1996-10-28 |
| Genre | : Science |
| ISBN | : 9813104961 |
This volume is intended to help graduate-level students of Continuum Mechanics become more proficient in its applications through the solution of analytical problems. Published as two separate books — Part I on Theory and Problems with Part II providing Solutions to the problems — professors may also find it quite useful in preparing their lectures and examinations. Part I includes a brief theoretical treatment for each of the major areas of Continuum Mechanics (fluid mechanics, thermodynamics, elastic and inelastic solids, electricity, dimensional analysis, and so on), as well as the references for further reading. The bulk of Part II consists of about 1000 solved problems. The book includes bibliographical references and index.
| Author | : Le Xuan Anh |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 284 |
| Release | : 2003-04-23 |
| Genre | : Computers |
| ISBN | : 9783540006541 |
This book addresses the general theory of motion of mechanical systems with Coulomb friction. In particular, the book focuses on the following specific problems: i) derivation of the equations of motion, ii) Painleve's paradoxes, iii) tangential impact and dynamic seizure, and iiii) frictional self-excited oscillations. In addition to theoretical results, the book contains a detailed description of experiments that have been performed. These show that, in general, the friction force at the instant of transition to motion is determined by the rate of tangential load and does not depend on the duration of the previous contact. These results are used to develop the theory of frictional self-excited oscillations. A number of industrially relevant mechanisms are considered, including the Painleve-Klein scheme, epicyclic mechanisms, crank mechanisms, gear transmission, the link mechanism of a planing machine, and the slider of metal-cutting machine tools. The book is intended for researchers, engineers and students in mechanical engineering.
| Author | : J. N. Reddy |
| Publisher | : Cambridge University Press |
| Total Pages | : 479 |
| Release | : 2013-07-29 |
| Genre | : Science |
| ISBN | : 1107292409 |
This best-selling textbook presents the concepts of continuum mechanics in a simple yet rigorous manner. It introduces the invariant form as well as the component form of the basic equations and their applications to problems in elasticity, fluid mechanics and heat transfer, and offers a brief introduction to linear viscoelasticity. The book is ideal for advanced undergraduates and graduate students looking to gain a strong background in the basic principles common to all major engineering fields, and for those who will pursue further work in fluid dynamics, elasticity, plates and shells, viscoelasticity, plasticity, and interdisciplinary areas such as geomechanics, biomechanics, mechanobiology and nanoscience. The book features derivations of the basic equations of mechanics in invariant (vector and tensor) form and specification of the governing equations to various co-ordinate systems, and numerous illustrative examples, chapter summaries and exercise problems. This second edition includes additional explanations, examples and problems.
| Author | : A. Bedford |
| Publisher | : |
| Total Pages | : 128 |
| Release | : 1985 |
| Genre | : Mathematics |
| ISBN | : |
