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SUMMARY:Noether's theorem  for quasi conservative mechanical systems
DTSTART;VALUE=DATE-TIME:20110406T160000Z
DTEND;VALUE=DATE-TIME:20110406T170000Z
DTSTAMP;VALUE=DATE-TIME:20261009T201943Z
UID:indico-event-141@indico.ipb.ac.rs
DESCRIPTION:If Lagrange's equations for nonconservative systems by introdu
 cing a Lagrangian\, which is equal to product of some function of time $f(
 t)$ and primary Lagrangian\, can be reduced to Euler-Lagrange's equations\
 , such mechanical systems are named quasi-conservative ones. The condition
  that some mom-conservative system can be considered as quasi-conservative
  one is the existence of at least one particular solution\, which results 
 from a system of $n$ differential equations with one unknown function -- t
 he cited function $f(t)$. For such systems the energy relations are studie
 d on the basis of corresponding Lagrange's equations\, and it is demonstra
 ted that under certain conditions\, the some integrals of motion equivalen
 t to Vujanovic's energy like conservation laws are valid.In this communica
 tion the corresponding energy relations are studied from a different\, mor
 e general variant\, on the basis of the corresponding accommodated Noether
 's theorem. Such Noether's theorem for quasi-conservative systems is formu
 lated\, starting from the total variation of action and the corresponding 
 Lagrange's equations and repeating the usual procedure. It differs from th
 e usual Noether's theorem only by presence of the new Lagrangian\, extende
 d from the primary one by the function $f(t)$ and by means of which the co
 rresponding condition for the existence of the integrals of motion (the so
 -called basic Noether's identity) is formulated. It is transformed to a mo
 re suitable form\, from which under certain conditions the corresponding i
 ntegrals of motions are obtained\, and for their existence\, it is necessa
 ry that at least one particular solution of one partial differential equat
 ion exists. The obtained results are in full accordance with the results o
 btained on the basis of Lagrange's equations\, and so modified Noether's t
 heorem is equivalent to Vujanović-Djukić's formulation of this theorem f
 or nonconservative systems\, obtained by transformation of D'Alambert-Lagr
 ange's principle. \n\nhttps://events.saifa.rs/event/141/
LOCATION:Mathematical Institute 301 F
URL:https://events.saifa.rs/event/141/
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