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Titlebook: Classical Planar Scattering by Coulombic Potentials; Markus Klein,Andreas Knauf Book 1992 Springer-Verlag Berlin Heidelberg 1992 Chaotic S

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发表于 2025-3-21 18:22:55 | 显示全部楼层 |阅读模式
书目名称Classical Planar Scattering by Coulombic Potentials
编辑Markus Klein,Andreas Knauf
视频video
丛书名称Lecture Notes in Physics Monographs
图书封面Titlebook: Classical Planar Scattering by Coulombic Potentials;  Markus Klein,Andreas Knauf Book 1992 Springer-Verlag Berlin Heidelberg 1992 Chaotic S
描述Astronomy as well as molecular physics describe non-relativistic motion by an interaction of the same form: By Newton‘s respectively by Coulomb‘s potential. But whereas the fundamental laws of motion thus have a simple form, the n-body problem withstood (for n > 2) all attempts of an explicit solution. Indeed, the studies of Poincare at the end of the last century lead to the conclusion that such an explicit solution should be impossible. Poincare himselfopened a new epoch for rational mechanics by asking qual­ itative questions like the one about the stability of the solar system. To a largeextent, his work, which was critical for the formation of differential geometry and topology, was motivated by problems arising in the analysis of the n-body problem ([38], p. 183). As it turned out, even by confining oneselfto questions ofqualitativenature, the general n-body problem could not be solved. Rather, simplified models were treated, like planar motion or the restricted 3-body problem, where the motion of a test particle did not influence the other two bodies.
出版日期Book 1992
关键词Chaotic Scattering; Chaotische Streuung; Coulomb-artige Singularitäten; Coulombic Singularity; Different
版次1
doihttps://doi.org/10.1007/978-3-540-47336-7
isbn_softcover978-3-662-13900-4
isbn_ebook978-3-540-47336-7Series ISSN 0940-7677
issn_series 0940-7677
copyrightSpringer-Verlag Berlin Heidelberg 1992
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发表于 2025-3-21 21:26:37 | 显示全部楼层
Book 1992n-body problem ([38], p. 183). As it turned out, even by confining oneselfto questions ofqualitativenature, the general n-body problem could not be solved. Rather, simplified models were treated, like planar motion or the restricted 3-body problem, where the motion of a test particle did not influence the other two bodies.
发表于 2025-3-22 03:40:58 | 显示全部楼层
0940-7677 omb‘s potential. But whereas the fundamental laws of motion thus have a simple form, the n-body problem withstood (for n > 2) all attempts of an explicit solution. Indeed, the studies of Poincare at the end of the last century lead to the conclusion that such an explicit solution should be impossibl
发表于 2025-3-22 07:38:03 | 显示全部楼层
Introduction to Requirements Management,ry 2.8). On the other hand, the bounded orbits . important since they influence the structure of those scattering states which have a long time delay. Lemma 7.4 gives a first example of a global observable (the topological entropy) which is determined entirely by the bounded orbits.
发表于 2025-3-22 10:11:46 | 显示全部楼层
The Distribution of the Closed Orbits,ry 2.8). On the other hand, the bounded orbits . important since they influence the structure of those scattering states which have a long time delay. Lemma 7.4 gives a first example of a global observable (the topological entropy) which is determined entirely by the bounded orbits.
发表于 2025-3-22 13:23:03 | 显示全部楼层
The Scattering Transformation, := ℝ. (. for . ≠ .). To control the asymptotic behaviour, we assume that . decomposes into the sum of a Coulombic potential and a short range potential. By this we mean the following: . A smooth, real-valued function . on the . . is called . if
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Introduction to Requirements Engineering,In this chapter we are to analyse the positive energy periodic orbits. The basic technique is to minimize the energy functional on the infinite-dimensional manifold of .-curves . : . → M, with . ≔[0,1]. As we shall see, this approach gives us full qualitative information for . large.
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