The Inverse Problem In Newtonian Mechanics
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Foundations Of Theoretical Mechanics
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Author : Ruggero Maria Santilli
language : en
Publisher: Springer
Release Date : 1978
Foundations Of Theoretical Mechanics written by Ruggero Maria Santilli and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 1978 with Mathematics categories.
Foundations Of Theoretical Mechanics I
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Author : Ruggero Maria Santilli
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-11-21
Foundations Of Theoretical Mechanics I written by Ruggero Maria Santilli and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-11-21 with Science categories.
The objective of this monograph is to present some methodological foundations of theoretical mechanics that are recommendable to graduate students prior to, or jointly with, the study of more advanced topics such as statistical mechanics, thermodynamics, and elementary particle physics. A program of this nature is inevitably centered on the methodological foundations for Newtonian systems, with particular reference to the central equations of our theories, that is, Lagrange's and Hamilton's equations. This program, realized through a study of the analytic representations in terms of Lagrange's and Hamilton's equations of generally nonconservative Newtonian systems (namely, systems with Newtonian forces not necessarily derivable from a potential function), falls within the context of the so-called Inverse Problem, and consists of three major aspects: l. The study of the necessary and sufficient conditions for the existence of a Lagrangian or Hamiltonian representation of given equations of motion with arbitrary forces; 2. The identification of the methods for the construction of a Lagrangian or Hamiltonian from given equations of motion verifying conditions 1; and 3 The analysis of the significance of the underlying methodology for other aspects of Newtonian Mechanics, e. g. , transformation theory, symmetries, and first integrals for nonconservative Newtonian systems. This first volume is devoted to the foundations of the Inverse Problem, with particular reference to aspects I and 2.
Foundations Of Theoretical Mechanics Ii
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Author : Ruggero Maria Santilli
language : en
Publisher: Springer
Release Date : 2012-04-09
Foundations Of Theoretical Mechanics Ii written by Ruggero Maria Santilli and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-04-09 with Science categories.
In the preceding volume,l I identified necessary and sufficient conditions for the existence of a representation of given Newtonian systems via a variational principle, the so-called conditions of variational self-adjointness. A primary objective of this volume is to establish that all Newtonian systems satisfying certain locality, regularity, and smoothness conditions, whether conservative or nonconservative, can be treated via conventional variational principles, Lie algebra techniques, and symplectic geometrical formulations. This volume therefore resolves a controversy on the repre sentational capabilities of conventional variational principles that has been 2 lingering in the literature for over a century, as reported in Chart 1. 3. 1. The primary results of this volume are the following. In Chapter 4,3 I prove a Theorem of Direct Universality of the Inverse Problem. It establishes the existence, via a variational principle, of a representation for all Newtonian systems of the class admitted (universality) in the coordinates and time variables of the experimenter (direct universality). The underlying analytic equations turn out to be a generalization of conventional Hamilton equations (those without external terms) which: (a) admit the most general possible action functional for first-order systems; (b) possess a Lie algebra structure in the most general possible, regular realization of the product; and (c) 1 Santilli (1978a). As was the case for Volume I, the references are listed at the end of this volume, first in chronological order and then in alphabetic order.
The Inverse Problem In Newtonian Mechanics
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Author : Ruggero Maria Santilli
language : en
Publisher:
Release Date : 1978
The Inverse Problem In Newtonian Mechanics written by Ruggero Maria Santilli and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1978 with Inverse problems (Differential equations) categories.
Modern Approach To Classical Mechanics A Second Edition
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Author : Harald Iro
language : en
Publisher: World Scientific Publishing Company
Release Date : 2015-08-21
Modern Approach To Classical Mechanics A Second Edition written by Harald Iro and has been published by World Scientific Publishing Company this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-08-21 with Science categories.
In this book we describe the evolution of Classical Mechanics from Newton's laws via Lagrange's and Hamilton's theories with strong emphasis on integrability versus chaotic behavior.In the second edition of the book we have added historical remarks and references to historical sources important in the evolution of classical mechanics.
Classical And Quantum Physics
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Author : G. Marmo
language : en
Publisher: Springer Nature
Release Date : 2019-10-26
Classical And Quantum Physics written by G. Marmo and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-10-26 with Science categories.
This proceedings is based on the interdisciplinary workshop held in Madrid, 5-9 March 2018, dedicated to Alberto Ibort on his 60th birthday. Alberto has great and significantly contributed to many fields of mathematics and physics, always with highly original and innovative ideas.Most of Albertos’s scientific activity has been motivated by geometric ideas, concepts and tools that are deeply related to the framework of classical dynamics and quantum mechanics.Let us mention some of the fields of expertise of Alberto Ibort:Geometric Mechanics; Constrained Systems; Variational Principles; Multisymplectic structures for field theories; Super manifolds; Inverse problem for Bosonic and Fermionic systems; Quantum Groups, Integrable systems, BRST Symmetries; Implicit differential equations; Yang-Mills Theories; BiHamiltonian Systems; Topology Change and Quantum Boundary Conditions; Classical and Quantum Control; Orthogonal Polynomials; Quantum Field Theory and Noncommutative Spaces; Classical and Quantum Tomography; Quantum Mechanics on phase space; Wigner-Weyl formalism; Lie-Jordan Algebras, Classical and Quantum; Quantum-to-Classical transition; Contraction of Associative Algebras; contact geometry, among many others.In each contribution, one may find not only technical novelties but also completely new way of looking at the considered problems. Even an experienced reader, reading Alberto's contributions on his field of expertise, will find new perspectives on the considered topic.His enthusiasm is happily contagious, for this reason he has had, and still has, very bright students wishing to elaborate their PhD thesis under his guidance.What is more impressive, is the broad list of rather different topics on which he has contributed.
The Geometry Of Ordinary Variational Equations
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Author : Olga Krupkova
language : en
Publisher: Springer
Release Date : 2006-11-14
The Geometry Of Ordinary Variational Equations written by Olga Krupkova and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-11-14 with Mathematics categories.
The book provides a comprehensive theory of ODE which come as Euler-Lagrange equations from generally higher-order Lagrangians. Emphasis is laid on applying methods from differential geometry (fibered manifolds and their jet-prolongations) and global analysis (distributions and exterior differential systems). Lagrangian and Hamiltonian dynamics, Hamilton-Jacobi theory, etc., for any Lagrangian system of any order are presented. The key idea - to build up these theories as related with the class of equivalent Lagrangians - distinguishes this book from other texts on higher-order mechanics. The reader should be familiar with elements of differential geometry, global analysis and the calculus of variations.
Proceedings Of The Iutam Symposium On Optimal Guidance And Control For Autonomous Systems 2023
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Author : Dilmurat Azimov
language : en
Publisher: Springer Nature
Release Date : 2024-01-05
Proceedings Of The Iutam Symposium On Optimal Guidance And Control For Autonomous Systems 2023 written by Dilmurat Azimov and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-01-05 with Technology & Engineering categories.
This book showcases a collection of papers that present cutting-edge studies, methods, experiments, and applications in various interdisciplinary fields. These fields encompass optimal control, guidance, navigation, game theory, stability, nonlinear dynamics, robotics, sensor fusion, machine learning, and autonomy. The chapters reveal novel studies and methods, providing fresh insights into the field of optimal guidance and control for autonomous systems. The book also covers a wide range of relevant applications, showcasing how optimal guidance and control techniques can be effectively applied in various domains, including mechanical and aerospace engineering. From robotics to sensor fusion and machine learning, the papers explore the practical implications of these techniques and methodologies.
Relativity And Gravitation Classical And Quantum Proceedings Of The 7th Latin American Symposium On Relativity And Gravitation Silarg Vii
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Author : Michael P Ryan Jr
language : en
Publisher: World Scientific
Release Date : 1991-08-12
Relativity And Gravitation Classical And Quantum Proceedings Of The 7th Latin American Symposium On Relativity And Gravitation Silarg Vii written by Michael P Ryan Jr and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 1991-08-12 with categories.
The Latin American Symposium on Relativity and Gravitation has been held every two or three years over the past twenty years. This is the seventh in the series.
Error Estimates For Advanced Galerkin Methods
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Author : Marcus Olavi Rüter
language : en
Publisher: Springer Nature
Release Date : 2019-11-07
Error Estimates For Advanced Galerkin Methods written by Marcus Olavi Rüter and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-11-07 with Science categories.
This monograph provides a compendium of established and novel error estimation procedures applied in the field of Computational Mechanics. It also includes detailed derivations of these procedures to offer insights into the concepts used to control the errors obtained from employing Galerkin methods in finite and linearized hyperelasticity. The Galerkin methods introduced are considered advanced methods because they remedy certain shortcomings of the well-established finite element method, which is the archetypal Galerkin (mesh-based) method. In particular, this monograph focuses on the systematical derivation of the shape functions used to construct both Galerkin mesh-based and meshfree methods. The mesh-based methods considered are the (conventional) displacement-based, (dual-)mixed, smoothed, and extended finite element methods. In addition, it introduces the element-free Galerkin and reproducing kernel particle methods as representatives of a class of Galerkin meshfree methods. Including illustrative numerical examples relevant to engineering with an emphasis on elastic fracture mechanics problems, this monograph is intended for students, researchers, and practitioners aiming to increase the reliability of their numerical simulations and wanting to better grasp the concepts of Galerkin methods and associated error estimation procedures.