Vol.3, No 15, 2003 pp.1133-1138
UDC 531.3
Invited Paper
THE GENERALIZED LAGRANGE'S EQUATIONS
OF THE SECOND KIND AND THE FIELD METHOD
FOR THEIR INTEGRATION
Ivana Kovačić
Faculty of Technical Sciences, Trg Dositeja Obradovica 6, Department
of Mechanics, 21121 Novi Sad, Serbia and Montenegro
Abstract. This paper presents the complete process of obtaining
motion of a mechanical system with variable mass subject to non-holonomic
constraints which are non-linear or of the first or higher order. Firstly,
the generalized Lagrange's equations of the second kind are extended to
a non-holonomic system with variable mass by introducing generalized reactive
forces. Then, the field method is applied to these equations of motion
to find their solution. Finally, an illustrative example showing the use
of this algorithm is given.
GENERALIZACIJA LAGRANGE-OVIH JEDNAČINA
DRUGE VRSTE I METODA POLJA ZA NJIHOVU INTEGRACIJU
Ovaj rad prezentuje kompletan proces dobijanja rešenja kretanja mehaničkog
sistema sa promenljivom masom i neholonomnim vezama koje su nelinearne,
te prvog ili višeg reda. U radu su najpre Lagranževe jednačine druge vrste
proširene na neholonomne sisteme sa promenljivom masom uvođenjem generalisanih
reaktivnih sila. Zatim je na ove jednačine primenjena metoda polja u cilju
nalaženja njihovog rešenja. Konačno, dat je primer koji ilustruje prezentovan
algoritam rešavanja.
