Books on the topic 'Principe de Hamilton'
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1
Bedford, Anthony. Hamilton’s Principle in Continuum Mechanics. Cham: Springer International Publishing, 2021. http://dx.doi.org/10.1007/978-3-030-90306-0.
2
Bedford, A. Hamilton's principle in continuum mechanics. Boston: Pitman Advanced Publishing Program, 1985.
3
Mann, Peter. Canonical & Gauge Transformations. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198822370.003.0018.
Abstract:
In this chapter, the Hamilton–Jacobi formulation is discussed in two parts: from a generating function perspective and as a variational principle. The Poincaré–Cartan 1-form is derived and solutions to the Hamilton–Jacobi equations are discussed. The canonical action is examined in a fashion similar to that used for analysis in previous chapters. The Hamilton–Jacobi equation is then shown to parallel the eikonal equation of wave mechanics. The chapter discusses Hamilton’s principal function, the time-independent Hamilton–Jacobi equation, Hamilton’s characteristic function, the rectification theorem, the Maupertius action principle and the Hamilton–Jacobi variational problem. The chapter also discusses integral surfaces, complete integral hypersurfaces, completely separable solutions, the Arnold–Liouville integrability theorem, general integrals, the Cauchy problem and de Broglie–Bohm mechanics. In addition, an interdisciplinary example of medical imaging is detailed.
4
Bedford, Anthony M. Hamiltons Principle in Continuum Mechanics. Wiley & Sons, Incorporated, John, 1986.
5
The Hamilton-Type Principle in Fluid Dynamics. Vienna: Springer-Verlag, 2006. http://dx.doi.org/10.1007/3-211-34324-5.
6
Palacios, Angel Fierros. The Hamilton-Type Principle in Fluid Dynamics. Springer, 2008.
7
Coopersmith, Jennifer. Hamiltonian Mechanics. Oxford University Press, 2017. http://dx.doi.org/10.1093/oso/9780198743040.003.0007.
Abstract:
Hamilton’s genius was to understand what were the true variables of mechanics (the “p − q,” conjugate coordinates, or canonical variables), and this led to Hamilton’s Mechanics which could obtain qualitative answers to a wider ranger of problems than Lagrangian Mechanics. It is explained how Hamilton’s canonical equations arise, why the Hamiltonian is the “central conception of all modern theory” (quote of Schrödinger’s), what the “p − q” variables are, and what phase space is. It is also explained how the famous conservation theorems arise (for energy, linear momentum, and angular momentum), and the connection with symmetry. The Hamilton-Jacobi Equation is derived using infinitesimal canonical transformations (ICTs), and predicts wavefronts of “common action” spreading out in (configuration) space. An analogy can be made with geometrical optics and Huygen’s Principle for the spreading out of light waves. It is shown how Hamilton’s Mechanics can lead into quantum mechanics.
8
Wright, Robert E. Hamilton Unbound. Greenwood Publishing Group, Inc., 2002. http://dx.doi.org/10.5040/9798400661044.
Abstract:
Modern financial theories enable us to look at old problems in early American Republic historiography from new perspectives. Concepts such as information asymmetry, portfolio choice, and principal-agent dilemmas open up new scholarly vistas. Transcending the ongoing debates over the prevalence of either community or capitalism in early America, Wright offers fresh and compelling arguments that illuminate motivations for individual and collective actions, and brings agency back into the historical equation. Wright argues that the Colonial rebellion was in part sparked by destabilizing British monetary policy that threatened many with financial insolvency; that in areas without modern financial institutions and practices, dueling was a rational means of protecting one's creditworthiness; that the principle-agent problem led to the institutionalization of the U.S. Constitution's system of checks and balances; and that a lack of information and education induced women to shift from active business owners to passive investors. Economists, historians, and political scientists alike will be interested in this strikingly novel and compelling recasting of our nation's formative decades.
9
Bedford, Anthony. Hamilton's Principle in Continuum Mechanics. Springer International Publishing AG, 2021.
10
Mann, Peter. Hamilton’s Principle in Phase Space. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198822370.003.0015.
Abstract:
This chapter derives Hamilton’s equations using the Legendre transform and the definition of the Hamiltonian function. While, in the Newtonian formalism, conservation laws were rather difficult to tease out, the Lagrangian formalism revolutionised the way of looking at them; however, the Hamiltonian formalism is perhaps even simpler than the Lagrangian formalism, making it straightforward to identify conservation laws and the symmetries of the system associated with each conserved property. In this chapter, the Hamiltonian is treated as being explicitly dependent on time, as this form is more general and will lead to an important relation that, although not an equation of motion, is still useful to discuss. The chapter also introduces Routhian mechanics as a symplectic reduction technique, using integrals of the motion.
11
Bedford, Anthony. Hamilton's Principle in Continuum Mechanics. Springer International Publishing AG, 2022.
12
Horing, Norman J. Morgenstern. Schwinger Action Principle and Variational Calculus. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198791942.003.0004.
Abstract:
Chapter 4 introduces the Schwinger Action Principle, along with associated particle and potential sources. While the methods described here originally arose in the relativistic quantum field theory of elementary particle physics, they have also profoundly advanced our understanding of non-relativistic many-particle physics. The Schwinger Action Principle is a quantum-mechanical variational principle that closely parallels the Hamilton Principle of Least Action of classical mechanics, generalizing it to include the role of quantum operators as generalized coordinates and momenta. As such, it unifies all aspects of quantum theory, incorporating Hamilton equations of motion for those operators and the Heisenberg equation, as well as producing the canonical equal-time commutation/anticommutation relations. It yields dynamical coupled field equations for the creation and annihilation operators of the interacting many-body system by variational differentiation of the Hamiltonian with respect to the field operators. Also, equations for the development of matrix elements (underlying Green’s functions) are derived using variations with respect to particle and potential “sources” (and coupling strength). Variational calculus, involving impressed potentials, c-number coordinates and fields, also quantum operator coordinates and fields, is discussed in full detail. Attention is given to the introduction of fermion and boson particle sources and their use in variational calculus.
13
Mann, Peter. The Stationary Action Principle. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198822370.003.0007.
Abstract:
This crucial chapter focuses on the stationary action principle. It introduces Lagrangian mechanics, using first-order variational calculus to derive the Euler–Lagrange equation, and the inverse problem is described. The chapter then considers the Ostrogradsky equation and discusses the properties of the extrema using the second-order variation to the action. It then discusses the difference between action functions (of Dirichlet boundary conditions) and action functionals of the extremal path. The different types of boundary conditions (Dirichlet vs Neumann) are elucidated. Topics discussed include Hessian conditions, Douglas’s theorem, the Jacobi last multiplier, Helmholtz conditions, Noether-type variation and Frenet–Serret frames, as well as concepts such as on shell and off shell. Actions of non-continuous extremals are examined using Weierstrass–Erdmann corner conditions, and the action principle is written in the most general form as the Hamilton–Suslov principle. Important applications of the Euler–Lagrange formulation are highlighted, including protein folding.
14
Coopersmith, Jennifer. The Lazy Universe. Oxford University Press, 2017. http://dx.doi.org/10.1093/oso/9780198743040.001.0001.
Abstract:
Action and the Principle of Least Action are explained: what Action is, why the Principle of Least Action works, why it underlies all physics, and what are the insights gained into energy, space, and time. The physical and mathematical origins of the Lagrange Equations, Hamilton’s Equations, the Lagrangian, the Hamiltonian, and the Hamilton-Jacobi Equation are shown. Also, worked examples in Lagrangian and Hamiltonian Mechanics are given. However the aim is to explain physics rather than to give a technical mastery of the subject. Therefore, much of the mathematics is in the appendices. While there is still some mathematics in the main text, the reader may select whether to work through, skim-read, or skip over it: the “story-line” will just about be maintained whatever route is chosen. The work is a much-reduced and simplified version of the outstanding text, “The Variational Principles of Mechanics” written by Cornelius Lanczos in 1949. That work is barely known today, and the present work may be considered as a tiny stepping-stone toward it. A principle that underlies all of physics will have wider repercussions; it is also to be appreciated in an aesthetic sense. It is hoped that this book will lead the reader to the widest possible understanding of the Principle of Least Action. Ideas such as Variational Mechanics, phase space, Fermat’s Principle, and Noether’s Theorem are explained.
15
Mann, Peter. Virtual Work & d’Alembert’s Principle. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198822370.003.0013.
Abstract:
This chapter discusses virtual work, returning to the Newtonian framework to derive the central Lagrange equation, using d’Alembert’s principle. It starts off with a discussion of generalised force, applied force and constraint force. Holonomic constraints and non-holonomic constraint equations are then investigated. The corresponding principles of Gauss (Gauss’s least constraint) and Jourdain are also documented and compared to d’Alembert’s approach before being generalised into the Mangeron–Deleanu principle. Kane’s equations are derived from Jourdain’s principle. The chapter closes with a detailed covering of the Gibbs–Appell equations as the most general equations in classical mechanics. Their reduction to Hamilton’s principle is examined and they are used to derive the Euler equations for rigid bodies. The chapter also discusses Hertz’s least curvature, the Gibbs function and Euler equations.
16
Palacios, Angel Fierros. Hamilton-Type Principle in Fluid Dynamics: Fundamentals and Applications to Magnetohydrodynamics, Thermodynamics, and Astrophysics. Springer London, Limited, 2006.
17
Coopersmith, Jennifer. Antecedents. Oxford University Press, 2017. http://dx.doi.org/10.1093/oso/9780198743040.003.0002.
Abstract:
Early ideas about optimization principles were brought in by an eclectic group of extraordinary thinkers: the Ancients (Hero, and Princess Dido), Fermat with his Principle of Least Time, the Bernoullis, Leibniz, Maupertuis, Euler, and d’Alembert. Also, Stevin was the first to invoke the impossibility of perpetual motion in a proof, and Huygens was the first to put Galilean Relativity to a quantitative test. The Swiss family of mathematical geniuses, the Bernoullis, tackled isoperimetric problems, such as the brachystochrone, and Johann Bernoulli discovered the Principle of Virtual Velocities. The flavour of the eighteenth century is shown in the evocative tale of the König affair, and the correspondence between Daniel Bernoulli and Euler. It is shown how symmetry arguments, leading ultimately to an energy-analysis, were competing with Newton’s force-analysis. The Principle of Least Action and Variational Mechanics, proper, were developed by Lagrange, Hamilton, and Jacobi.
18
Palacios, Angel Fierros. The Hamilton-Type Principle in Fluid Dynamics: Fundamentals and Applications to Magnetohydrodynamics, Thermodynamics, and Astrophysics. Springer, 2006.
19
T. Michaltsos, George, and Ioannis G. Raftoyiannis, eds. Bridges’ Dynamics. BENTHAM SCIENCE PUBLISHERS, 2012. http://dx.doi.org/10.2174/97816080522021120101.
Abstract:
Bridges’ Dynamics covers the historical review of research and introductory mathematical concepts related to the structural dynamics of bridges. The e-book explains the theory behind engineering aspects such as 1) dynamic loadings, 2) mathematical concepts (calculus elements of variations, the d’ Alembert principle, Lagrange’s equation, the Hamilton principle, the equations of Heilig, and the δ and H functions), 3) moving loads, 4) bridge support mechanics (one, two and three span beams), 5) Static systems under dynamic loading 6) aero-elasticity, 7) space problems (2D and 3D) and 8) absorb systems (equations governing the behavior of the bridge-absorber system). The e-book is a useful introductory textbook for civil engineers interested in the theory of bridge structures.
20
Mann, Peter. Liouville’s Theorem & Classical Statistical Mechanics. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198822370.003.0020.
Abstract:
This chapter returns to the discussion of constrained Hamiltonian dynamics, now in the canonical setting, including topics such as regular Lagrangians, constraint surfaces, Hessian conditions and the constrained action principle. The standard approach to Hamiltonian mechanics is to treat all the variables as being independent; in the constrained case, a constraint function links the variables so they are no longer independent. In this chapter, the Dirac–Bergmann theory for singular Lagrangians is developed, using an action-based approach. The chapter then investigates consistency conditions and Dirac’s different types of constraints (i.e. first-class constraints, second-class constraints, primary constraints and secondary constraints) before deriving the Dirac bracket from simple arguments. The Jackiw–Fadeev constraint formulation is then discussed before the chapter closes with the Güler formulation for a constrained Hamilton–Jacobi theory.
21
Mill, John Stuart. An Examination of Sir William Hamilton's Philosophy and of the Principle Philosophical Questions Discussed in His Writings (Collected Works of John Stuart Mill). Classic Books, 2000.
22
Coopersmith, Jennifer. Lagrangian Mechanics. Oxford University Press, 2017. http://dx.doi.org/10.1093/oso/9780198743040.003.0006.
Abstract:
It is demonstrated how d’Alembert’s Principle can be used as the basis for a more general mechanics – Lagrangian Mechanics. How this leads to Hamilton’s Principle (the Principle of Least Action) is shown mathematically and in words. It is further explained why Lagrangian Mechanics is so general, why forces of constraint may be ignored, and how external conditions lead to “curved space.” Also, it is explained why the Lagrangian, L, has the form L = T − V (where T is the kinetic energy and V is the potential energy), and why T is in “quadratic form” (T = 1/2mv2). It is shown how Noether’s Theorem leads to a more fundamental definition of energy and links the conservation of energy to the homogeneity of time. The ingenious Lagrange multipliers are explained, and also generalized forces and generalized coordinates.
23
Kates, Nick, and Ellen Anderson. Canadian Approach to Integrated Care. Edited by Robert E. Feinstein, Joseph V. Connelly, and Marilyn S. Feinstein. Oxford University Press, 2017. http://dx.doi.org/10.1093/med/9780190276201.003.0003.
Abstract:
This chapter describes the evolution of collaborative mental health care in Canada over the past 15 years, and the ways in which integrated care is becoming an increasingly integral part of Canada’s provincial and territorial healthcare services. It explores the underlying principles and models that can be found across the country. There is a particular emphasis on three things: (1) changes any mental health service can make to improve collaboration, (2) programs to increase the mental health skills and capacity of primary care, and (3) the integration of mental health services within primary care.A program in Hamilton, Ontario, has successfully integrated mental health counselors and psychiatrists into the offices of 170 family physicians across a city of 500,000 people for the past 20 years. The authors present data from the program’s evaluation, as well as key lessons learned and advice for other programs looking to set up similar models.
24
Basdevant, Jean-Louis. Variational Principles in Physics. Springer, 2010.
25
Basdevant, Jean-Louis. Variational Principles in Physics. Springer London, Limited, 2007.
26
Calvo, Christopher W. The Emergence of Capitalism in Early America. University Press of Florida, 2020. http://dx.doi.org/10.5744/florida/9780813066332.001.0001.
Abstract:
The first comprehensive examination of early American economic thought in over a generation, The Emergence of Capitalism in Early America challenges the traditional narrative that Americans were born committed to the principles of Adam Smith. Americans are shown to have developed a distinct brand of hybrid capitalism, suited to the nation’s unique political, intellectual, cultural, and economic histories. Given America’s primary position in the history of capitalism, its economists were well situated to comment on market phenomenon. Covering a broad range of the period’s economic literature and offering close analyses of the antebellum reception of Smith’s Wealth of Nations, this book rescues America’s first economists from historical neglect. In thematically organized chapters, the intellectual cultures of American protectionism and free trade are examined. Protectionism exercised enormous influence in the discourse, constituting what rightly has been called an ‘American political economy.’ Henry Carey is highlighted as the central thinker in protectionist thought, providing an economic blueprint for the nation’s future industrial and commercial supremacy. Sharp regional divisions existed among the nation’s strongest proponents of free-trade ideology, namely Calhoun, Wayland, McVickar, Vethake, Cardozo, and Cooper, as well as important theoretical distinctions with Smithian-inspired laissez-faire. In a separate chapter, American conservative economists—among others, Fitzhugh and Holmes—are positioned alongside antebellum socialists—Skidmore and Byllesby—illustrating the rather awkward ideological arrangements attendant to emergent capitalism. Finally, the tricky relationship Americans have held with financial institutions is explored. Beginning with Hamilton, this book analyzes the financial literature as Americans learned to live with arguably the most complex and misunderstood manifestation of capitalism—finance.
27
Horing, Norman J. Morgenstern. Interacting Electron–Hole–Phonon System. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198791942.003.0011.
Abstract:
Chapter 11 employs variational differential techniques and the Schwinger Action Principle to derive coupled-field Green’s function equations for a multi-component system, modeled as an interacting electron-hole-phonon system. The coupled Fermion Green’s function equations involve five interactions (electron-electron, hole-hole, electron-hole, electron-phonon, and hole-phonon). Starting with quantum Hamilton equations of motion for the various electron/hole creation/annihilation operators and their nonequilibrium average/expectation values, variational differentiation with respect to particle sources leads to a chain of coupled Green’s function equations involving differing species of Green’s functions. For example, the 1-electron Green’s function equation is coupled to the 2-electron Green’s function (as earlier), also to the 1-electron/1-hole Green’s function, and to the Green’s function for 1-electron propagation influenced by a nontrivial phonon field. Similar remarks apply to the 1-hole Green’s function equation, and all others. Higher order Green’s function equations are derived by further variational differentiation with respect to sources, yielding additional couplings. Chapter 11 also introduces the 1-phonon Green’s function, emphasizing the role of electron coupling in phonon propagation, leading to dynamic, nonlocal electron screening of the phonon spectrum and hybridization of the ion and electron plasmons, a Bohm-Staver phonon mode, and the Kohn anomaly. Furthermore, the single-electron Green’s function with only phonon coupling can be rewritten, as usual, coupled to the 2-electron Green’s function with an effective time-dependent electron-electron interaction potential mediated by the 1-phonon Green’s function, leading to the polaron as an electron propagating jointly with its induced lattice polarization. An alternative formulation of the coupled Green’s function equations for the electron-hole-phonon model is applied in the development of a generalized shielded potential approximation, analysing its inverse dielectric screening response function and associated hybridized collective modes. A brief discussion of the (theoretical) origin of the exciton-plasmon interaction follows.
28
Basdevant, Jean-Louis. Variational Principles in Physics. Springer International Publishing AG, 2023.
29
Basdevant, Jean-Louis. Variational Principles in Physics. Springer, 2006.