Another New Solvable Many-Body Model of Goldfish Type
Vernadsky National Library of Ukraine
Переглянути архів Інформація| Поле | Співвідношення | |
| Title |
Another New Solvable Many-Body Model of Goldfish Type
|
|
| Creator |
Calogero, F.
|
|
| Description |
A new solvable many-body problem is identified. It is characterized by nonlinear Newtonian equations of motion (''acceleration equal force'') featuring one-body and two-body velocity-dependent forces ''of goldfish type'' which determine the motion of an arbitrary number N of unit-mass point-particles in a plane. The N (generally complex) values zn(t) at time t of the N coordinates of these moving particles are given by the N eigenvalues of a time-dependent N×N matrix U(t) explicitly known in terms of the 2N initial data zn(0) and z˙n(0). This model comes in two different variants, one featuring 3 arbitrary coupling constants, the other only 2; for special values of these parameters all solutions are completely periodic with the same period independent of the initial data (''isochrony''); for other special values of these parameters this property holds up to corrections vanishing exponentially as t→∞ (''asymptotic isochrony''). Other isochronous variants of these models are also reported. Alternative formulations, obtained by changing the dependent variables from the N zeros of a monic polynomial of degree N to its N coefficients, are also exhibited. Some mathematical findings implied by some of these results – such as Diophantine properties of the zeros of certain polynomials – are outlined, but their analysis is postponed to a separate paper.
|
|
| Date |
2019-02-18T13:04:40Z
2019-02-18T13:04:40Z 2012 |
|
| Type |
Article
|
|
| Identifier |
Another New Solvable Many-Body Model of Goldfish Type / C. Calogero // Symmetry, Integrability and Geometry: Methods and Applications. — 2012. — Т. 8. — Бібліогр.: 16 назв. — англ.
1815-0659 2010 Mathematics Subject Classification: 37J35; 37C27; 70F10; 70H08 DOI: http://dx.doi.org/10.3842/SIGMA.2012.046 http://dspace.nbuv.gov.ua/handle/123456789/148460 |
|
| Language |
en
|
|
| Relation |
Symmetry, Integrability and Geometry: Methods and Applications
|
|
| Publisher |
Інститут математики НАН України
|
|