The principle of possible mixing of the system. Perfect connections

The principle of possible mixing of the system. Perfect connections

D.A. Zakirova

Before examining the possible displacement of the system, let us describe the possible displacement of the point.

Any infinitesimal displacement that satisfies the boundary constraints of a point at a given time is called a possible displacement. Let’s designate the possible displacement of a point by a vector. denote by the projections of the vector on the coordinate axis; these quantities are also called point coordinate variations. In this case, the possible displacement vector can be expressed in terms of variations in the coordinates of the point as follows:

The possible displacements of the points that make up the system are called the possible displacements of the system. Possible offsets of points of the system must satisfy the following two conditions:1. Possible displacements of points of the system must be infinitesimal. If these movements are limited, the system will move to another state, and the equilibrium state of the system will change.2. All connections to the system must be preserved in the eventual movement of the points of the system. When the connection is broken, the appearance of the system will change.   The number of independent motions of a system in a fixed holonomic constraint is called the degree of freedom of this system. If we denote by k-the degree of freedom of a system consisting of n points under the action of an S-holonomic connection,can be written as k = 3n -S.Let us briefly name the elementary work of this force on the possible displacement of the point of application of the active force and designate it as the possible work of the force. In this case, according to the main job description: the formula fits. Ties in which the forces acting on a mechanical system of n points are equal to zero are called ideal ties. Ideal connections can be expressed as follows: – reaction force applied to the system


A smooth plane is an example of a perfect connection.Equal links are called non-start links, and inequality links are called start links. The equation of links includes only the coordinates of points, such links are called holonomic (or geometric) links … If the links depend on time, these links are called non-stationary linksReferences:1.P. Shohaidarova. Sh. Shoziyotov. Sh. Zoirov. “Theoretical Mechanics”, textbook. 1991 year2. T.R. Rashidov. “Foundations of Theoretical Mechanics”. 1990 year