Results 201 to 210 of about 21,173,420 (246)
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Foundations of Physics Letters, 1993
The dynamics of N bodies in a gravitational field is shown to be calculable by the decomposition method.
Antonio Ambrosetti, Vittorio Coti Zelati
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The dynamics of N bodies in a gravitational field is shown to be calculable by the decomposition method.
Antonio Ambrosetti, Vittorio Coti Zelati
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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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The Integral Manifolds of the N Body Problem
Journal of Dynamics and Differential Equations, 2021The \(N\)-\textit{body problem} refers to the study of the dynamics of a system of \(N\) point masses, moving under their mutual gravitational attraction. For such a system, it is a classical fact that there are conserved quantities of center of mass, linear momentum, angular momentum and energy.
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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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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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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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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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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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Towards an Adaptive Treecode for N-body Problems
Journal of Scientific Computing, 2020zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Benjamin W. Ong, Satyen Dhamankar
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