Mechanics is a branch of physics, inwhich studies the movement of bodies, as well as the interaction between these material bodies. This section of physics includes dynamics - one of the subsections of mechanics, which is devoted to the study of the causes of the occurrence of mechanical motion. One of the main principles of dynamics is the principle of d'Alembert. It enables the formulation of dynamic problems through statics, which greatly facilitates the calculations.
Dynamic tasks are often addressed throughlaws of Newton. However, this is not the only way. The principles of mechanics for solving such problems are developed - these are some initial assumptions underlying the methods of solving dynamic problems. One of these principles is the D'Alembert principle, which is interconnected with the kinetostatics method. This method is one of the ways to solve dynamic problems, which is based on writing dynamic equations in the form of equilibrium equations. The method of kinetostatics finds application in the theory of mechanisms and machines, the resistance of materials (sopromat), in other areas of theoretical mechanics. It is used to simplify the solution of a number of general technical problems. The most convenient for solving the first problem of dynamics (the definition of the acting force or one of several forces on the material point, provided that its mass and motion are given).
The principle of d'Alembert, or else it is called the principlekinetostatics, can be used both for a material point, and for a mechanical system. This principle allows us to apply methods for solving statics for solving dynamic problems. A material point is a body whose dimensions are assumed to be zero, but its mass is preserved. D'Alembert made a proposal that implied a conditional application of the inertia force to the body, which moves with acceleration, i.e., actively accelerates. In this case, the system of forces that act on the point becomes balanced, which allows us to solve the dynamics problems using the equations of statics. The d'Alembert principle for a material point is formulated as follows:
If to a non-free material point, movingunder the action of applied active forces and reaction forces of bonds, to apply its force of inertia, then at any given time the resulting system of forces will be balanced, that is, the geometric sum of these forces will be zero.
In other words, if the forces acting on the material point are conditionally added to the force of its inertia, then the result is a balanced system.
There is a definite order of solving problems using the principle of kinetostatics, the d'Alembert principle. The following sequence of actions is performed:
Механической системой называется общность material points provided that their movements are interrelated. A more detailed definition says that a mechanical system is a collection, a community of material points that move according to the laws of classical mechanics, while they interact not only with each other, but also with bodies that are not part of a given set of points. The d'Alembert principle for the mechanical system is as follows:
For a moving mechanical system in anythe moment of time, the geometric sum of the principal vectors of the external forces, the reactions of the bonds, the forces of inertia is zero, and the geometric sum of the principal moments from external forces, coupling reactions, inertia forces is zero.
For a mechanical system (as for a materialpoints) of the equation of motion can be written as equilibrium equations, from which later unknown quantities (forces) can be determined, including the reactions of bonds. Derived formulas for solving problems using the d'Alembert principle are second-order differential equations in connection with the fact that in each of them there is an acceleration, which is the second derivative of the law of motion of the point of the body.
Принципом аналитической статики называется the principle of possible displacements is the Lagrange principle. This principle, more precisely its formulation, says that for a system to be balanced it is necessary and sufficient that the sum of the work of forces that are applied to the system should be zero for any possible displacement of the system accompanied by its exit from the equilibrium state.
The d'Alembert principle and the Lagrange principle are not difficultcombine in one, which allows us to express the general equation of dynamics. As a result, we obtain an equation for a system with ideal constraints. The d'Alembert-Lagrange principle is formulated as follows:
When the mechanical system moves with idealconnections at each moment of time, the sum of the elementary jobs of all the applied active forces and inertia forces on any possible displacement of the system will be zero.
From the general equation of dynamics it is possible to deduce allstated in the theoretical mechanics of the dynamics theorem. This equation puts the work of inertia forces and the work of active forces on a level of importance, that is, these works are treated on an equal basis with each other.
