Abstract
In order to give an insight into the work of the machine before the production and assembly and to obtain good analysis, this paper presents detailed solutions to the specific problem occured in the field of analytical mechanics. In addition to numerical procedures in the paper, a review of the theoretical foundations was made.Various types of analysis are very common in mechanical engineering, due to the possibility of an approximation of complex machines. For the proposed system, Lagrange's equations of the first kind, covariant and contravariant equations, Hamiltons equations and the generalized coordinates, as well as insight in Coulumb friction force are provided.Also, the conditions of static equilibrium are solved numerically and using intersection of the two curves. Finally, stability of motion for the disturbed and undisturbed system was investigated.
Highlights
Extent analysis of the mechanical systemhas been one of the most fundamental and challenging tasks, that has been largely studied for decades
Where the projection of the normal reaction N2, is not a negative value, and the second when it is.Bearing in mind that normal force,as part of the friction force, figures in the explicit expressions for the xv and yv, v = 1,2,3, whereby it is the function of xv and yv, v = 1,2,3, by itself, it is necessary to determine its sign at the initial time.By solving differential equations of motion on a small time interval,for two separate cases, for the N2 mutually close values of the same sign have been gotten
In the beginning of this paper, using the example of a simple mechanical construction model with constrained motion, we have proved that it is possible to perform an analysis of the motion of a mechanical systemby applying Lagrange's equations of the first and second kind, as well as Hamilton's equations
Summary
Extent analysis of the mechanical systemhas been one of the most fundamental and challenging tasks, that has been largely studied for decades. The problems considered in the present paper involve a review of references on the specific types of systems - holonomic systems. Our paper suggests a different approach for modelling a specific multi-body system, including the special investigation of modelling Coulomb friction force, the problem that so far has hardly been considered. Unlike the papers [8] and [9], where the relative advantages and disadvantages of various analytical methods of nonholonomic systems are briefly presented, the problem of the instability of the equilibrium state of a scleronomic mechanical system with linear homogeneous constraints are considered in [10], and the problem of the stability of the equilibrium state in the case with holonomic mechanical systems in [11].
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