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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| Date: | 2004 |
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| Format: | Article |
| Language: | English |
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Інститут прикладної математики і механіки НАН України
2004
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| Series: | Механика твердого тела |
| Online Access: | http://dspace.nbuv.gov.ua/handle/123456789/123757 |
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| Journal Title: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Cite this: | 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 |
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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 |
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AT vujicicveljkoa programmedmotionofmechanicalsystems |
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2023-10-18T20:44:52Z |
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2023-10-18T20:44:52Z |
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1796151005042180096 |