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- Title
EXTENDED LAGRANGIAN FORMALISM FOR RHEONOMIC SYSTEMS WITH VARIABLE MASS.
- Authors
Mušicki, Djordje
- Abstract
In this paper the extended Lagrangian formalism for the rheonomic systems (Dj. Muˇsicki, 2004), which began with the modification of the mechanics of such systems (V. Vujiˇci´c, 1987), is extended to the systems with variable mass, with emphasis on the corresponding energy relations. This extended Lagrangian formalism is based on the extension of the set of chosen generalized coordinates by new quantities, suggested by the form of nonstationary constraints, which determine the position of the frame of reference in respect to which these generalized coordinates refer. As a consequence, an extended system of the Lagrangian equations is formulated, accommodated to the variability of the masses of particles, where the additional ones correspond to the additional generalized coordinates. By means of these equations, the energy relations of such systems have been studied, where it is demonstrated that here there are four types of energy conservation laws. The obtained energy laws are more complete and natural than the corresponding ones in the usual Lagrangian formulation for such systems. It is demonstrated that the obtained energy laws, are in full accordance with the energy laws in the corresponding vector formulation, if they are expressed in terms of the quantities introduced in this formulation of mechanics. The obtained results are illustrated by an example: the motion of a rocket, which ejects the gasses backwards, while this rocket moves up a straight line on an oblique plane, which glides uniformly in a horizontal direction.
- Subjects
RHEONOMIC constraints; VARIABLE mass systems; LAGRANGE equations; ENERGY conservation laws; NOETHER'S theorem
- Publication
Theoretical & Applied Mechanics, 2017, Vol 44, Issue 1, p115
- ISSN
1450-5584
- Publication type
Article
- DOI
10.2298/TAM170601006M