Lobachevskii Journal of Mathematics
RUS  ENG    JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB  
General information
Latest issue
Archive

Search papers
Search references

RSS
Latest issue
Current issues
Archive issues
What is RSS



Lobachevskii J. Math.:
Year:
Volume:
Issue:
Page:
Find






Personal entry:
Login:
Password:
Save password
Enter
Forgotten password?
Register


Lobachevskii Journal of Mathematics, 2006, Volume 24, Pages 73–134 (Mi ljm13)  

A geometric study of many body systems

E. Straume

Norwegian University of Science and Technology
References:
Abstract: An $n$-body system is a labelled collection of $n$ point masses in a Euclidean space, and their congruence and internal symmetry properties involve a rich mathematical structure which is investigated in the framework of equivariant Riemannian geometry. Some basic concepts are $n$-configuration, configuration space, internal space, shape space, Jacobi transformation and weighted root system. The latter is a generalization of the root system of $SU(n)$, which provides a bookkeeping for expressing the mutual distances of the point masses in terms of the Jacobi vectors. Moreover, its application to the study of collinear central $n$-configurations yields a simple proof of Moulton's enumeration formula. A major topic is the study of matrix spaces representing the shape space of $n$-body configurations in Euclidean $k$-space, the structure of the $m$-universal shape space and its $O(m)$-equivariant linear model. This also leads to those “orbital fibrations”, where $SO(m)$ or $O(m)$ act on a sphere with a sphere as orbit space. A few of these examples are encountered in the literature, e.g. the special case $S^5/O(2)\approx S^4$ was analyzed independently by Arnold, Kuiper and Massey in the 1970's.
Submitted by: V. V. Lychagin
Received: 30.10.2006
Bibliographic databases:
Language: English
Citation: E. Straume, “A geometric study of many body systems”, Lobachevskii J. Math., 24 (2006), 73–134
Citation in format AMSBIB
\Bibitem{Str06}
\by E.~Straume
\paper A geometric study of many body systems
\jour Lobachevskii J. Math.
\yr 2006
\vol 24
\pages 73--134
\mathnet{http://mi.mathnet.ru/ljm13}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=2292227}
\zmath{https://zbmath.org/?q=an:1109.70011}
Linking options:
  • https://www.mathnet.ru/eng/ljm13
  • https://www.mathnet.ru/eng/ljm/v24/p73
  • Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    Lobachevskii Journal of Mathematics
     
      Contact us:
     Terms of Use  Registration to the website  Logotypes © Steklov Mathematical Institute RAS, 2024