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Titlebook: Mathematical Methods of Classical Mechanics; V. I. Arnold Textbook 1989Latest edition Springer-Verlag New York 1989 Lagrangian mechanics.M

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书目名称Mathematical Methods of Classical Mechanics
编辑V. I. Arnold
视频video
丛书名称Graduate Texts in Mathematics
图书封面Titlebook: Mathematical Methods of Classical Mechanics;  V. I. Arnold Textbook 1989Latest edition Springer-Verlag New York 1989 Lagrangian mechanics.M
描述In this text, the author constructs the mathematical apparatus of classical mechanics from the beginning, examining all the basic problems in dynamics, including the theory of oscillations, the theory of rigid body motion, and the Hamiltonian formalism. This modern approch, based on the theory of the geometry of manifolds, distinguishes iteself from the traditional approach of standard textbooks. Geometrical considerations are emphasized throughout and include phase spaces and flows, vector fields, and Lie groups. The work includes a detailed discussion of qualitative methods of the theory of dynamical systems and of asymptotic methods like perturbation techniques, averaging, and adiabatic invariance.
出版日期Textbook 1989Latest edition
关键词Lagrangian mechanics; Mathematische Physik; Mechanik; Rigid body; Vector field; classical mechanics; diffe
版次2
doihttps://doi.org/10.1007/978-1-4757-2063-1
isbn_softcover978-1-4419-3087-3
isbn_ebook978-1-4757-2063-1Series ISSN 0072-5285 Series E-ISSN 2197-5612
issn_series 0072-5285
copyrightSpringer-Verlag New York 1989
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Rigid bodies, first because they were solved by Euler and Lagrange, and also because we live in three-dimensional euclidean space, so that most of the mechanical systems with a finite number of degrees of freedom which we are likely to encounter consist of rigid bodies.
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Introduction to perturbation theoryetely solvable “unperturbed” problems. These methods can be easily justified if we are investigating motion over a small interval of time. Relatively little is known about how far we can trust the conclusions of perturbation theory in investigating motion over large or infinite intervals of time.
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ces on behavior. Many of us think the answer is yes (Bouchard & Propping, 1993). Work with monozygotic twins reared apart provides an imperfect, but nevertheless powerful window on the direct influence of genes on whole organisms. Extended behavior genetics designs that include twins also provide im
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978-1-4419-3087-3Springer-Verlag New York 1989
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Mathematical Methods of Classical Mechanics978-1-4757-2063-1Series ISSN 0072-5285 Series E-ISSN 2197-5612
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Investigation of the equations of motionIn most cases (for example, in the three-body problem) we can neither solve the system of differential equations nor completely describe the behavior of the solutions. In this chapter we consider a few simple but important problems for which Newton’s equations can be solved.
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