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Mathematical Methods Of Classical Mechanics
Mathematical Methods of Classical Mechanics is a classic graduate textbook by the mathematician Vladimir I. Arnold. It was originally written in Russian, but was translated into English by A. Weinstein and K. Vogtmann. Contents * Part I: Newtonian Mechanics ** Chapter 1: Experimental Facts ** Chapter 2: Investigation of the Equations of Motion * Part II: Lagrangian Mechanics ** Chapter 3: Variational Principles ** Chapter 4: Lagrangian Mechanics on Manifolds ** Chapter 5: Oscillations ** Chapter 6: Rigid Bodies * Part III: Hamiltonian Mechanics ** Chapter 7: Differential forms ** Chapter 8: Symplectic Manifolds ** Chapter 9: Canonical Formalism ** Chapter 10: Introduction to Perturbation Theory * Appendices ** Riemannian curvature ** Geodesics of left-invariant metrics on Lie groups and the hydrodynamics of ideal fluids ** Symplectic structures on algebraic manifolds ** Contact structures ** Dynamical systems with symmetries ** Normal forms of quadratic Hamiltonians ** Norma ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Vladimir I
Vladimir I may refer to: * Vladimir I of Kiev Vladimir I Sviatoslavich or Volodymyr I Sviatoslavych ( orv, Володимѣръ Свѧтославичь, ''Volodiměrъ Svętoslavičь'';, ''Uladzimir'', russian: Владимир, ''Vladimir'', uk, Володимир, ''Volodymyr''. Se ... (c. 958 – 1015) * Vladimir I of Novgorod (1020–1052) {{hndis, Vladimir 01 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Vogtmann
Karen Vogtmann (born July 13, 1949 in Pittsburg, California''Biographies of Candidates 2002.'' . September 2002, Volume 49, Issue 8, pp. 970–981) is an American mathematician working primarily in the area of geometric group theory. She is known for having introduced, in a 1986 paper with , an object now known as the [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Lagrangian Mechanics
In physics, Lagrangian mechanics is a formulation of classical mechanics founded on the stationary-action principle (also known as the principle of least action). It was introduced by the Italian-French mathematician and astronomer Joseph-Louis Lagrange in his 1788 work, '' Mécanique analytique''. Lagrangian mechanics describes a mechanical system as a pair (M,L) consisting of a configuration space M and a smooth function L within that space called a ''Lagrangian''. By convention, L = T - V, where T and V are the kinetic and potential energy of the system, respectively. The stationary action principle requires that the action functional of the system derived from L must remain at a stationary point (a maximum, minimum, or saddle) throughout the time evolution of the system. This constraint allows the calculation of the equations of motion of the system using Lagrange's equations. Introduction Suppose there exists a bead sliding around on a wire, or a swinging simple p ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Calculus Of Variations
The calculus of variations (or Variational Calculus) is a field of mathematical analysis that uses variations, which are small changes in functions and functionals, to find maxima and minima of functionals: mappings from a set of functions to the real numbers. Functionals are often expressed as definite integrals involving functions and their derivatives. Functions that maximize or minimize functionals may be found using the Euler–Lagrange equation of the calculus of variations. A simple example of such a problem is to find the curve of shortest length connecting two points. If there are no constraints, the solution is a straight line between the points. However, if the curve is constrained to lie on a surface in space, then the solution is less obvious, and possibly many solutions may exist. Such solutions are known as ''geodesics''. A related problem is posed by Fermat's principle: light follows the path of shortest optical length connecting two points, which depends up ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Rigid Body
In physics, a rigid body (also known as a rigid object) is a solid body in which deformation is zero or so small it can be neglected. The distance between any two given points on a rigid body remains constant in time regardless of external forces or moments exerted on it. A rigid body is usually considered as a continuous distribution of mass. In the study of special relativity, a perfectly rigid body does not exist; and objects can only be assumed to be rigid if they are not moving near the speed of light. In quantum mechanics, a rigid body is usually thought of as a collection of point masses. For instance, molecules (consisting of the point masses: electrons and nuclei) are often seen as rigid bodies (see classification of molecules as rigid rotors). Kinematics Linear and angular position The position of a rigid body is the position of all the particles of which it is composed. To simplify the description of this position, we exploit the property that the body is rigi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Hamiltonian Mechanics
Hamiltonian mechanics emerged in 1833 as a reformulation of Lagrangian mechanics. Introduced by Sir William Rowan Hamilton, Hamiltonian mechanics replaces (generalized) velocities \dot q^i used in Lagrangian mechanics with (generalized) ''momenta''. Both theories provide interpretations of classical mechanics and describe the same physical phenomena. Hamiltonian mechanics has a close relationship with geometry (notably, symplectic geometry and Poisson structures) and serves as a link between classical and quantum mechanics. Overview Phase space coordinates (p,q) and Hamiltonian H Let (M, \mathcal L) be a mechanical system with the configuration space M and the smooth Lagrangian \mathcal L. Select a standard coordinate system (\boldsymbol,\boldsymbol) on M. The quantities \textstyle p_i(\boldsymbol,\boldsymbol,t) ~\stackrel~ / are called ''momenta''. (Also ''generalized momenta'', ''conjugate momenta'', and ''canonical momenta''). For a time instant t, the Legendre transformat ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Differential Form
In mathematics, differential forms provide a unified approach to define integrands over curves, surfaces, solids, and higher-dimensional manifolds. The modern notion of differential forms was pioneered by Élie Cartan. It has many applications, especially in geometry, topology and physics. For instance, the expression is an example of a -form, and can be integrated over an interval contained in the domain of : :\int_a^b f(x)\,dx. Similarly, the expression is a -form that can be integrated over a surface : :\int_S (f(x,y,z)\,dx\wedge dy + g(x,y,z)\,dz\wedge dx + h(x,y,z)\,dy\wedge dz). The symbol denotes the exterior product, sometimes called the ''wedge product'', of two differential forms. Likewise, a -form represents a volume element that can be integrated over a region of space. In general, a -form is an object that may be integrated over a -dimensional manifold, and is homogeneous of degree in the coordinate differentials dx, dy, \ldots. On an -dimensional manifold, ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Nauka (publisher)
Nauka (russian: Наука, lit. trans.: ''Science'') is a Russian publisher of academic books and journals. Established in the USSR in 1923, it was called the USSR Academy of Sciences Publishing House until 1963. Until 1934 the publisher was based in Leningrad, then moved to Moscow. Its logo depicts an open book with Sputnik 1 above it. Nauka was the main scientific publisher of the USSR. Structurally it was a complex of publishing institutions, printing and book selling companies. It had two departments (in Leningrad and Novosibirsk) with separate printing works, two main editorial offices (for physical and mathematical literature and oriental literature) and more than 50 thematic editorial offices. Nauka's main book selling company ''Akademkniga'' ("Academic Book" in English) had some 30 trading centers in all major cities of the country. Nauka was the main publisher of the USSR Academy of Sciences and its branches. The greater part of Nauka's production were monographs. It al ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Bulletin Of The American Mathematical Society
The ''Bulletin of the American Mathematical Society'' is a quarterly mathematical journal published by the American Mathematical Society. Scope It publishes surveys on contemporary research topics, written at a level accessible to non-experts. It also publishes, by invitation only, book reviews and short ''Mathematical Perspectives'' articles. History It began as the ''Bulletin of the New York Mathematical Society'' and underwent a name change when the society became national. The Bulletin's function has changed over the years; its original function was to serve as a research journal for its members. Indexing The Bulletin is indexed in Mathematical Reviews, Science Citation Index, ISI Alerting Services, CompuMath Citation Index, and Current Contents/Physical, Chemical & Earth Sciences. See also *'' Journal of the American Mathematical Society'' *''Memoirs of the American Mathematical Society'' *''Notices of the American Mathematical Society'' *'' Proceedings of the American M ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Project Euclid
Project Euclid is a collaborative partnership between Cornell University Library and Duke University Press which seeks to advance scholarly communication in theoretical and applied mathematics and statistics through partnerships with independent and society publishers. It was created to provide a platform for small publishers of scholarly journals to move from print to electronic in a cost-effective way. Through a combination of support by subscribing libraries and participating publishers, Project Euclid has made 70% of its journal articles available as open access. As of 2010, Project Euclid provided access to over one million pages of open-access content. Mission and goals Project Euclid's stated mission is to advance scholarly communication in the field of theoretical and applied mathematics and statistics. Through a "mixture of open access, subscription, and hosted subscription content it provides a way for small publishers (especially societies) to host their math or statistic ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
SAO/NASA ADS
The SAO/NASA Astrophysics Data System (ADS) is an online database of over 16 million astronomy and physics papers from both peer reviewed and non-peer reviewed sources. Abstracts are available free online for almost all articles, and full scanned articles are available in Graphics Interchange Format (GIF) and Portable Document Format (PDF) for older articles. It was developed by the National Aeronautics and Space Administration (NASA), and is managed by the Smithsonian Astrophysical Observatory. ADS is a powerful research tool and has had a significant impact on the efficiency of astronomical research since it was launched in 1992. Literature searches that previously would have taken days or weeks can now be carried out in seconds via the ADS search engine, which is custom-built for astronomical needs. Studies have found that the benefit to astronomy of the ADS is equivalent to several hundred million US dollars annually, and the system is estimated to have tripled the readership ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
