As a separate science of theoretical mechanics is a doctrine that combines the general laws of motion and mechanical interaction of material bodies.The development of this science was originally received as a branch of physics, based on axioms, it is available in a separate branch of science.
Solving problems on the dynamics within the subject of theoretical mechanics greatly facilitated by the use of the principle of D'Alembert.It consists in that the active balancing of the forces which act on the point of the mechanical system, and the existing links reactions occurs due account of the so-called inertial forces.Mathematically this is expressed as the summation of all of the above elements, the result is zero.
Himself Jean d'Alembert Leron (1717-1783), known to the world as a great educator, has achieved great achievements in various fields of science.Mathematics, mechanics, philosophy subjected to analysis of his inquiring mind.As a result of the works of D'Alembert touched the material systems (the principle of d'Alembert), describing their differential equations, namely the drafting of the rules.Jean Leron was justified perturbation theory of the planets, he paid much attention to the study of the theory of series and differential equations, mathematical analysis.A French national, D'Alembert became an honorary foreign member of the St. Petersburg Academy of Sciences.
merit scholar Frenchman who developed the principle of solving complex problems of dynamics, which also bears his name, lies in the fact that, thanks to its application for consideration of dynamic processes allowed to use simpler methods of statistical mechanics.Due to the simplicity and accessibility of this principle (the principle of d'Alembert) has found wide application in engineering practice.
apply the principle of d'Alembert for the material point
establish a unified approach, the algorithm study of a single mechanical system helps the principle of D'Alembert.This is not dependent on any conditions imposed on its movement.Dynamic differential equations of motion are reduced to the form of the equilibrium equations.For example, taking some to consider the non-free material point M, the traffic moves along the curve AB as a result of the active forces with resultant F, we may use the designation N for the reaction force (impact curve AB in M).Enter the force F, N, P to the basic equation describing the dynamics of a point, we obtain a convergent system, which expresses the equilibrium condition specific system.The value of F describes the effect of inertia and has a negative value.This is the use of the principle of D'Alembert in the calculations with respect to the material point.
Note that with this approach, we get quite a conditional equation relating force that is used to balance the system inertia.But despite this, the principle of D'Alembert provides a convenient and simple solution to the problems of dynamics.
application of the principle of d'Alembert for the mechanical system
Having achieved a positive result in the solution of problems of the dynamics of a material point, we can safely proceed to the more complex version of the problem, where the principle of d'Alembert for the mechanical system.
equation for the system is not much different from the equation for a point.The essential difference is that the calculation of mechanical constrained system at any time involves finding the resultant of all forces, the sum of responses relations and forces of inertia of mass points.
Using the above methods and principles in no way runs counter to the basic law of physics.On the contrary, even at a fraction of poached to facilitate the process of decision.This method did not appear out of nowhere, all the major conclusions are based on the fundamental laws of Newtonian principles-German Euler, which got its development in the principles of d'Alembert.
