Open AccessAn equilibrium position in the generalized mathematical model of a system of rigid bodies elastically mounted on an Euler-Bernoulli beam
Author(s) -
A. D. Mizhidon
Publication year - 2021
Publication title -
journal of physics. conference series
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.21
H-Index - 85
eISSN - 1742-6596
pISSN - 1742-6588
DOI - 10.1088/1742-6596/1847/1/012009
Subject(s) - position (finance) , coordinate system , bernoulli's principle , mechanical system , mathematics , euler's formula , beam (structure) , differential equation , generalized coordinates , mathematical analysis , classical mechanics , physics , computer science , geometry , thermodynamics , finance , artificial intelligence , optics , economics
The paper considers a generalized mathematical model of a class of mechanical systems, which represent systems of rigid bodies elastically mounted on an Euler-Bernoulli beam. This model has the form of a hybrid system of differential equations having a definite structure and describing the process of transfer (transition) of the system within the frames of some coordinated system chosen. On the basis of the generalized mathematical model, a generalized approach to finding the equilibrium position for mechanical systems, which belong to a given class of systems, in a chosen coordinate system has been proposed. The equilibrium position of a mechanical system is understood as the solution of a definite hybrid system of differential equations, furthermore, this solution does not change with time. The equilibrium position of a mechanical system within a given coordinate system allows one to proceed - by replacement of the variables - to consideration of the generalized mathematical model studied earlier and describing transfer of a system with respect to the equilibrium.