Results 261 to 270 of about 5,968,169 (345)
Some of the next articles are maybe not open access.
1995
Ours, according to Leibniz, is the best of all possible worlds, and the laws of nature can therefore be described in terms of extremal principles. Thus, arising from corresponding variational problems, the differential equations of mechanics have invariance properties relative to certain groups of coordinate transformations.
Carl Ludwig Siegel, Jürgen K. Moser
openaire +1 more source
Ours, according to Leibniz, is the best of all possible worlds, and the laws of nature can therefore be described in terms of extremal principles. Thus, arising from corresponding variational problems, the differential equations of mechanics have invariance properties relative to certain groups of coordinate transformations.
Carl Ludwig Siegel, Jürgen K. Moser
openaire +1 more source
2006
How do three celestial bodies move under their mutual gravitational attraction? This problem has been studied by Isaac Newton and leading mathematicians over the last two centuries. Poincaré's conclusion, that the problem represents an example of chaos in nature, opens the new possibility of using a statistical approach.
Mauri Valtonen, Hannu Karttunen
openaire +1 more source
How do three celestial bodies move under their mutual gravitational attraction? This problem has been studied by Isaac Newton and leading mathematicians over the last two centuries. Poincaré's conclusion, that the problem represents an example of chaos in nature, opens the new possibility of using a statistical approach.
Mauri Valtonen, Hannu Karttunen
openaire +1 more source
1996
Historically, the three-body problem is the most important problem of celestial mechanics and for about two centuries has also been the most extensively studied problem of the whole mathematical physics. In this chapter, we consider only the “classical” subjects, while the more “modern” ones (KAM theory, chaotic solutions, etc.) find their place in the
Dino Boccaletti, Giuseppe Pucacco
openaire +1 more source
Historically, the three-body problem is the most important problem of celestial mechanics and for about two centuries has also been the most extensively studied problem of the whole mathematical physics. In this chapter, we consider only the “classical” subjects, while the more “modern” ones (KAM theory, chaotic solutions, etc.) find their place in the
Dino Boccaletti, Giuseppe Pucacco
openaire +1 more source
2018
In Chap. 7, we have looked at two point masses that were moving under their mutual gravitational influence. Formally speaking we were dealing with two bodies each with six degrees of freedom (three position vector components and three velocity vector components).
openaire +1 more source
In Chap. 7, we have looked at two point masses that were moving under their mutual gravitational influence. Formally speaking we were dealing with two bodies each with six degrees of freedom (three position vector components and three velocity vector components).
openaire +1 more source
Gravitational Three-Body Problem
2014After solving the one- and two-body problems, generalizing to the three-body problem should be easy, right? No! In fact, it was the gravitational three-body problem that led Henri Poincare to discover dynamical “chaos.” Some systems are so sensitive to initial conditions that a tiny shift today can dramatically change the long-term behavior.
openaire +1 more source
American Journal of Physics, 1980
The simplest three-body problem that attracts physical interest is the one first studied by Euler. In Euler’s problem, a primary and secondary mass are fixed in space, a given distance apart, and a test mass is allowed to move unrestricted in their superimposed gravitational fields.
openaire +1 more source
The simplest three-body problem that attracts physical interest is the one first studied by Euler. In Euler’s problem, a primary and secondary mass are fixed in space, a given distance apart, and a test mass is allowed to move unrestricted in their superimposed gravitational fields.
openaire +1 more source
Dynamical model of binary asteroid systems through patched three-body problems
Celestial mechanics & dynamical astronomy, 2016F. Ferrari, M. Lavagna, K. Howell
semanticscholar +1 more source
Close-coupling approach to Coulomb three-body problems.
Physical Review Letters, 2002I. Bray
semanticscholar +1 more source
1972
The quantum mechanical three-body problem has been studied with increasing interest in the last decade. The main progress was achieved by deriving integral equations which are not only theoretically correct, but also practically applicable. Such equations allow us in particular to investigate, besides three-body bound states, the scattering of an ...
openaire +1 more source
The quantum mechanical three-body problem has been studied with increasing interest in the last decade. The main progress was achieved by deriving integral equations which are not only theoretically correct, but also practically applicable. Such equations allow us in particular to investigate, besides three-body bound states, the scattering of an ...
openaire +1 more source
Low Energy Transit Orbits in the Restricted Three-Body Problems
, 1968C. Conley
semanticscholar +1 more source