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Doctoral Thesis
DOI
https://doi.org/10.11606/T.45.1992.tde-20220712-114458
Document
Author
Full name
Sonia Regina Leite Garcia
E-mail
Institute/School/College
Knowledge Area
Date of Defense
Published
São Paulo, 1992
Supervisor
Title in Portuguese
Familias tipo hill
Keywords in Portuguese
Estabilidade De Sistemas
Abstract in Portuguese
não disponível
Title in English
not available
Abstract in English
In the paper a necessary and sufficient condition for the stability of the equilibrium ([03]), barone-netto, a and cesar, m o study the stability of the solution (x, 'X PONTO', y, 'Y PONTO') = (0,0,0,0) of a mechanical system of two degrees of freedom 'X 2 PONTOS' = -xf (x) (x,y) 'PERTENCE' r x r 'Y 2 PONTOS' = -yg (x) f,g,'PERTENCE' 'C POT.2', f (0)>0, g (0)>0, by using a function l: [0, 'X BARRA IND.0] 'seta' 'r barra' ASSOCIATE TO THE SYSTEM, AND ALSO EXHIBIT A FIRST INTEGRAL TO THE SYSTEM, 'w barra': U 'contido' 'r pot.4' 'seta r' WHERE U IS A NEIGHBORHOOD OF THE ORIGIN, WHICH DECIDES THE STABILITY. THE AUTHORS CHARACTERIZE THE STABILITY THROUGH CONDITIONS ON L, AND ALSO SHOW THAT THE SOLUTION (X, 'x ponto', Y, 'y ponto')= (0,0,0,0) IS STABLE IF AND ONLY IF 'w barra' IS A LIAPUNOV FUNCTION FOR THE STABILITY. IN OUR WORK, WE GENERALIZE THIS RESULT FOR A MECHANICAL SYSTEM OF N+1 DEGREES OF FREEDOM OF THE TYPE 'x 2 pontos = -xf (x) (x,y) 'PERTENCE' r x 'R POT.N' 'Y 2 PONTOS = -G (X)Y G= ['g ind.Ij'] 'pertence' 'c pot.2', f (0)>0. As in [03], we characterize the stability in this case through of a explicit liapunov function
 
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Publishing Date
2022-07-13
 
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