Results 281 to 290 of about 3,877,766 (328)
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Journal of Mathematical Physics, 2000
This selective review is written as an introduction to the mathematical theory of the Schrödinger equation for N particles. Characteristic for these systems are the cluster properties of the potential in configuration space, which are expressed in a simple geometric language. The methods developed over the last 40 years to deal with this primary aspect
Hunziker, W., Sigal, I. M.
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This selective review is written as an introduction to the mathematical theory of the Schrödinger equation for N particles. Characteristic for these systems are the cluster properties of the potential in configuration space, which are expressed in a simple geometric language. The methods developed over the last 40 years to deal with this primary aspect
Hunziker, W., Sigal, I. M.
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2009
Entry for Encyclopedia of Complexity and Systems Science.Article Outline: Glossary; Definition of the Subject; Introduction: Simple Choreographies and Relative Equilibria; Symmetry Groups and Equivariant Orbits; The 3-Body Problem; Minimizing Properties of Simple Choreographies; Generalized Orbits and Singularities; Asymptotic Estimates at Collisions ...
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Entry for Encyclopedia of Complexity and Systems Science.Article Outline: Glossary; Definition of the Subject; Introduction: Simple Choreographies and Relative Equilibria; Symmetry Groups and Equivariant Orbits; The 3-Body Problem; Minimizing Properties of Simple Choreographies; Generalized Orbits and Singularities; Asymptotic Estimates at Collisions ...
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2018
Abstract This chapter discusses the N-body problem. In 1886, Karl Weierstrass submitted the following question to the scientific community on the occasion of a mathematical competition to mark the 60th birthday of King Oscar II of Sweden.
Nathalie Deruelle, Jean-Philippe Uzan
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Abstract This chapter discusses the N-body problem. In 1886, Karl Weierstrass submitted the following question to the scientific community on the occasion of a mathematical competition to mark the 60th birthday of King Oscar II of Sweden.
Nathalie Deruelle, Jean-Philippe Uzan
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1997
Suppose that two points (r 1, m 1) and (r 2, m 2) mutually interact with potential energy U(|r 1 − r 2|), so that the equations of motion have the form \({m_1}{\ddot r_1} = - \frac{{\partial U}}{{\partial {r_1}}},\;{m_2}{\ddot r_2} = - \frac{{\partial U}}{{\partial {r_2}}}.\)
V. I. Arnold +2 more
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Suppose that two points (r 1, m 1) and (r 2, m 2) mutually interact with potential energy U(|r 1 − r 2|), so that the equations of motion have the form \({m_1}{\ddot r_1} = - \frac{{\partial U}}{{\partial {r_1}}},\;{m_2}{\ddot r_2} = - \frac{{\partial U}}{{\partial {r_2}}}.\)
V. I. Arnold +2 more
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2016
When going from two bodies to three, or more, bodies, the complexity increases significantly, due to their mutual attractions. The two-body problem can be mathematically formulated so a closed-form solution is possible. With more than two bodies, it is impossible to formulate such a solution. There are some special cases, however, that can be handled.
Pini Gurfil, P. Kenneth Seidelmann
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When going from two bodies to three, or more, bodies, the complexity increases significantly, due to their mutual attractions. The two-body problem can be mathematically formulated so a closed-form solution is possible. With more than two bodies, it is impossible to formulate such a solution. There are some special cases, however, that can be handled.
Pini Gurfil, P. Kenneth Seidelmann
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AIP Conference Proceedings, 2008
The purpose of this note is to introduce some of the basic techniques in group theory to the study the symmetries of the Newtonian n‐body problem. The main tool is the representations of finite groups.
Zhihong Xia +3 more
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The purpose of this note is to introduce some of the basic techniques in group theory to the study the symmetries of the Newtonian n‐body problem. The main tool is the representations of finite groups.
Zhihong Xia +3 more
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1996
The order of the chapters, and thus the framework of our treatment, reflects the fact that we have followed the traditional route; that is, to examine first the two-body problem and then the N-body problem. In abstract terms, it might appear more sensible to proceed backwards, from arbitrary N to the particular case N = 2.
Dino Boccaletti, Giuseppe Pucacco
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The order of the chapters, and thus the framework of our treatment, reflects the fact that we have followed the traditional route; that is, to examine first the two-body problem and then the N-body problem. In abstract terms, it might appear more sensible to proceed backwards, from arbitrary N to the particular case N = 2.
Dino Boccaletti, Giuseppe Pucacco
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1974
Two years ago, in a lecture given at the Schladming Conference 1972, I reviewed the present status of the quantum mechanical three-body problem [1]. It was the main intention of this survey to illustrate the way in which the properties of the integral equations, studied in this field, are related to basic concepts of multichannel collision theory. Such
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Two years ago, in a lecture given at the Schladming Conference 1972, I reviewed the present status of the quantum mechanical three-body problem [1]. It was the main intention of this survey to illustrate the way in which the properties of the integral equations, studied in this field, are related to basic concepts of multichannel collision theory. Such
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Universal formulation for the N-body problem
Journal of Guidance, Control, and Dynamics, 1996Summary: The universal formulation for the perturbed two-body problem is generalized to cover all gravitational \(N\)-body problems involving a dominant central mass. Its efficiency, when compared to conventional numerical integration, is shown in several examples.
Zadunaisky, Pedro E. +1 more
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The Gravitational N-Body Problem
2019We now come to a relativistic formulation of the gravitational N-body problem which can be described exactly only in the frame of numerical relativity. In the general case not even the concept of a ‘body’ can be formulated rigorously because of the non-linearities of GR (the distinction between ‘self- and external-field’ of a body is a real problem).
Michael H. Soffel, Wen-Biao Han
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