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Computer visualization for the topology of integrable cases in rigid body dynamicsстатья
Информация о цитировании статьи получена из
Web of Science
Дата последнего поиска статьи во внешних источниках: 24 мая 2016 г.
- Автор: Fomenko A.T.
- Сборник: Computer Graphics International '98
- Год издания: 1998
- Место издания: Comp Graph Soc, HANNOVER, GERMANY
- Первая страница: 490
- Последняя страница: 503
- Аннотация: In modern applied mathematics the computer visualization is very often extremely useful for solution concrete mechanical and physical problems. Some methods of topological modeling fur visualization call be found, fur example, in the recent book of T.L. Kunii and A.T. Fomenko [1]. Many problems of modern geometry and topology, mathematical physics and mechanics are reduced to the analysis of symmetries of corresponding differential equations. In cases when the group of symmetries is large, it is usually possible to integrate the differential equations, i.e. to find the solutions of physical problem in "direct way". Recently the remarkable relation of this problem with topological bifurcation theory was discovered Ir turns out that classification of dynamical systems which have "the maximal symmetry group" can be given in terms of one-dimensional and two-dimensional topological objects [2]-[5]. Some of these results were obtained on the basis of computer visualization of the set of bifurcations appearing in integrable Hamiltonian systems. In the paper we illustrate this theory by visual material showing the bifurcations in concrete dynamical systems from classical mechanics.
- Добавил в систему: Фоменко Анатолий Тимофеевич