Programmed motion of mechanical systems

The main results of this contribution are new methods of solving of adjoint systems of 6n di erential nonlinear equations and its application in classical and celestial mechanics. At first, we are observing a general dynamic system of n differential equations of the first order, which contain n inde...

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Бібліографічні деталі
Дата:2004
Автор: Vujičić, Veljko A.
Формат: Стаття
Мова:English
Опубліковано: Інститут прикладної математики і механіки НАН України 2004
Назва видання:Механика твердого тела
Онлайн доступ:http://dspace.nbuv.gov.ua/handle/123456789/123757
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Назва журналу:Digital Library of Periodicals of National Academy of Sciences of Ukraine
Цитувати:Programmed motion of mechanical systems / Veljko A. Vujičić // Механика твердого тела: Межвед. сб. науч. тр. — 2004. — Вип. 34. — С. 199-208. — Бібліогр.: 5 назв. — англ.

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Digital Library of Periodicals of National Academy of Sciences of Ukraine
id irk-123456789-123757
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spelling irk-123456789-1237572017-09-10T03:04:17Z Programmed motion of mechanical systems Vujičić, Veljko A. The main results of this contribution are new methods of solving of adjoint systems of 6n di erential nonlinear equations and its application in classical and celestial mechanics. At first, we are observing a general dynamic system of n differential equations of the first order, which contain n independent functions x(t) and n unknown composite functions X(x(t)). A programme of motion of such one is described by n independent finite algebraic equations f(x) = 0. For realization of the control motion it is necessary to de ne functions X(x) and within them also control functions. It is shown that such dynamic systems do not correspond to mechanical systems. Defining of control motion of mechanical systems is much more complex. It is explained which of the di erential equations of motion are used, and what are the consequences. It is also manifested that 3N Newton's differential equations of motions and n = 3N−k, k < 3N, Lagrange's differential equations of second kind, or 2n Hamilton's differential equations on manifolds, are not giving the same results at defining of forces, being of the primary importance for control motion. 2004 Article Programmed motion of mechanical systems / Veljko A. Vujičić // Механика твердого тела: Межвед. сб. науч. тр. — 2004. — Вип. 34. — С. 199-208. — Бібліогр.: 5 назв. — англ. 0321-1975 http://dspace.nbuv.gov.ua/handle/123456789/123757 62-50 en Механика твердого тела Інститут прикладної математики і механіки НАН України
institution Digital Library of Periodicals of National Academy of Sciences of Ukraine
collection DSpace DC
language English
description The main results of this contribution are new methods of solving of adjoint systems of 6n di erential nonlinear equations and its application in classical and celestial mechanics. At first, we are observing a general dynamic system of n differential equations of the first order, which contain n independent functions x(t) and n unknown composite functions X(x(t)). A programme of motion of such one is described by n independent finite algebraic equations f(x) = 0. For realization of the control motion it is necessary to de ne functions X(x) and within them also control functions. It is shown that such dynamic systems do not correspond to mechanical systems. Defining of control motion of mechanical systems is much more complex. It is explained which of the di erential equations of motion are used, and what are the consequences. It is also manifested that 3N Newton's differential equations of motions and n = 3N−k, k < 3N, Lagrange's differential equations of second kind, or 2n Hamilton's differential equations on manifolds, are not giving the same results at defining of forces, being of the primary importance for control motion.
format Article
author Vujičić, Veljko A.
spellingShingle Vujičić, Veljko A.
Programmed motion of mechanical systems
Механика твердого тела
author_facet Vujičić, Veljko A.
author_sort Vujičić, Veljko A.
title Programmed motion of mechanical systems
title_short Programmed motion of mechanical systems
title_full Programmed motion of mechanical systems
title_fullStr Programmed motion of mechanical systems
title_full_unstemmed Programmed motion of mechanical systems
title_sort programmed motion of mechanical systems
publisher Інститут прикладної математики і механіки НАН України
publishDate 2004
url http://dspace.nbuv.gov.ua/handle/123456789/123757
citation_txt Programmed motion of mechanical systems / Veljko A. Vujičić // Механика твердого тела: Межвед. сб. науч. тр. — 2004. — Вип. 34. — С. 199-208. — Бібліогр.: 5 назв. — англ.
series Механика твердого тела
work_keys_str_mv AT vujicicveljkoa programmedmotionofmechanicalsystems
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last_indexed 2023-10-18T20:44:52Z
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