Adjoint variational principles for regularised conservative systems

2014 ◽  
Author(s):  
A. Thyagaraja
Keyword(s):  
Variational Principles ◽  
Conservative Systems

The Generalized Quasi-Variational Principles of NCS and Its Application in Mechanical Vibration

2007 ◽  
Author(s):  
Lifu Liang ◽  
Liming Dai ◽  
Qingyong Guo
Keyword(s):  
Phase Space ◽  
Variational Principles ◽  
Mechanical Vibration ◽  
Internal Force ◽  
Energy Principle ◽  
Force System ◽  
Conservative Systems ◽  
Generalized Displacements ◽  
Complementary Energy Principle ◽  
Two Kinds Of Variables

According to the corresponding relations between generalized forces and generalized displacements, the basic equations of elasto-dynamics in phase space are multiplied by corresponding virtual quantities, integrated and then added algebraically. By considering the character of fellow body and surface forces, the generalized quasi-variational principles of non-conservative systems are established in elasto-dynamics in phase space. By doing inverse Laplace transformation, the convolutional generalized quasi-variational principles of non-conservative systems of elasto-dynamics are established in original space. Applying the generalized quasi-complementary energy principle to the mechanical vibration problem of two kinds of variables, the authors of this paper present a calculation method for solving two kinds of variables simultaneously: the internal force and the displacement of a typical fellow force system.

Quasi-Variational Principles of Large Elastic Deformation in Non-Conservative Systems Based on Base Forces Theory and its Application

2008 ◽  
Author(s):  
Zongmin Liu ◽  
Lifu Liang ◽  
Tao Fan
Keyword(s):  
Elastic Deformation ◽  
Variational Principles ◽  
Analytic Solutions ◽  
Energy Principle ◽  
Conservative Systems ◽  
Generalized Displacements ◽  
Large Elastic Deformation ◽  
Base Forces ◽  
Basic Equations ◽  
Theory Framework

Based on base forces theory framework, the basic equations of time boundary value problem of large elastic deformation in non-conservative systems are defined. According to the corresponding relations between generalized forces and generalized displacements, the basic equations of elasto-dynamics are multiplied by corresponding virtual quantities, integrated and then added algebraically. Considering that both body forces and surface forces are fellow forces, the generalized Hamilton-type quasi-variational principles with three kinds of variables of large elastic deformation based on base forces theory in non-conservative systems are established. Then they are degenerated. Applying the Hamilton-type quasi-potential energy principle, analytic solutions of large deformation cantilever beam problem in non-conservative systems is obtained. Finally, some correlative problems are discussed.

Follower forces: Leipholz's researches into generalized variational principles

1990 ◽  
Vol 17 (3) ◽  
pp. 287-293 ◽  
Author(s):  
G. M. L. Gladwell
Keyword(s):  
Key Words ◽  
Variational Principles ◽  
Nonconservative Systems ◽  
Adjoint Systems ◽  
Conservative Systems ◽  
Generalized Variational Principles ◽  
Follower Forces

Classical variational principles, for conservative systems, are associated with the names of Lagrange and Hamilton. Generalized variational principles for nonconservative systems were introduced by various authors and in various physical contexts in the period 1945 – 1966. This review traces their development and their use, by Leipholz, in the period 1971 – 1986. Key words: follower forces, variational principles, generalized, nonconservative, adjoint systems, stability, divergence, flutter.

Variational Principles in Mathematical Physics, Geometry, and Economics

2009 ◽  
Author(s):  
Alexandru Kristaly ◽  
Vicentiu D. Radulescu ◽  
Csaba Varga
Keyword(s):  
Variational Principles ◽  
Mathematical Physics

A Finite Element Analysis of the General Rolling Contact Problem for a Viscoelastic Rubber Cylinder

1988 ◽  
Vol 16 (1) ◽  
pp. 18-43 ◽  
Author(s):  
J. T. Oden ◽  
T. L. Lin ◽  
J. M. Bass
Keyword(s):  
Finite Element ◽  
Variational Principles ◽  
Standing Waves ◽  
Rolling Contact ◽  
Finite Element Models ◽  
Viscoelastic Cylinder ◽  
Element Analysis ◽  
Elastic Rubber ◽  
Frictional Effects ◽  
Rough Foundation

Abstract Mathematical models of finite deformation of a rolling viscoelastic cylinder in contact with a rough foundation are developed in preparation for a general model for rolling tires. Variational principles and finite element models are derived. Numerical results are obtained for a variety of cases, including that of a pure elastic rubber cylinder, a viscoelastic cylinder, the development of standing waves, and frictional effects.

The Physical World

2017 ◽  
Author(s):  
Nicholas Manton ◽  
Nicholas Mee
Keyword(s):  
Quantum Mechanics ◽  
Particle Physics ◽  
Variational Principles ◽  
Black Body ◽  
Black Body Radiation ◽  
Physical World ◽  
Atomic Scale ◽  
Solid State Physics ◽  
Least Action ◽  
Dimensional Spacetime

The book is an inspirational survey of fundamental physics, emphasizing the use of variational principles. Chapter 1 presents introductory ideas, including the principle of least action, vectors and partial differentiation. Chapter 2 covers Newtonian dynamics and the motion of mutually gravitating bodies. Chapter 3 is about electromagnetic fields as described by Maxwell’s equations. Chapter 4 is about special relativity, which unifies space and time into 4-dimensional spacetime. Chapter 5 introduces the mathematics of curved space, leading to Chapter 6 covering general relativity and its remarkable consequences, such as the existence of black holes. Chapters 7 and 8 present quantum mechanics, essential for understanding atomic-scale phenomena. Chapter 9 uses quantum mechanics to explain the fundamental principles of chemistry and solid state physics. Chapter 10 is about thermodynamics, which is built around the concepts of temperature and entropy. Various applications are discussed, including the analysis of black body radiation that led to the quantum revolution. Chapter 11 surveys the atomic nucleus, its properties and applications. Chapter 12 explores particle physics, the Standard Model and the Higgs mechanism, with a short introduction to quantum field theory. Chapter 13 is about the structure and evolution of stars and brings together material from many of the earlier chapters. Chapter 14 on cosmology describes the structure and evolution of the universe as a whole. Finally, Chapter 15 discusses remaining problems at the frontiers of physics, such as the interpretation of quantum mechanics, and the ultimate nature of particles. Some speculative ideas are explored, such as supersymmetry, solitons and string theory.

Some variational principles associated with ODEs of maximal symmetry. Part 2: The general case

2018 ◽  
Vol 24 (2) ◽  
pp. 175-183
Author(s):  
Jean-Claude Ndogmo
Keyword(s):  
Explicit Form ◽  
Nonlinear Equations ◽  
Variational Principles ◽  
Symmetry Algebra ◽  
First Integrals ◽  
Maximal Symmetry ◽  
General Order ◽  
Linear And Nonlinear ◽  
Variational Symmetries ◽  
Variational Symmetry

Abstract Variational and divergence symmetries are studied in this paper for the whole class of linear and nonlinear equations of maximal symmetry, and the associated first integrals are given in explicit form. All the main results obtained are formulated as theorems or conjectures for equations of a general order. A discussion of the existence of variational symmetries with respect to a different Lagrangian, which turns out to be the most common and most readily available one, is also carried out. This leads to significantly different results when compared with the former case of the transformed Lagrangian. The latter analysis also gives rise to more general results concerning the variational symmetry algebra of any linear or nonlinear equations.

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