# What is the d’Alembert Principle and What Does It Mean?

June 27, 2021D’Alembert, in his work Traite de Dynamique, published in 1743, based all mechanics on the principles of “inertia, compound motion and balance between two bodies” and explained the basic principle that is called by his name today: “In a system, internal inertial forces and external forces that provide acceleration are explained. forces are equal, but in opposite directions”.

Dynamics is defined by the equations of motion established according to Newton’s second theory; If all the external forces acting on a system are not in balance, it will lead to acceleration. “D’Alembert’s principle” states that when the resultant of all external forces, mass times acceleration, is taken into account as a force (kinetic power), the system will be in equilibrium, that is, it can be studied as a static problem. This principle, which at first glance seems like a simple repetition of Newton’s theory, it not only facilitates the solution of problems, but also prepares the environment for the definition of mechanics with the variation method. Indeed, in dynamics problems, the moments of the forces around the center of mass have to be taken, whereas in statics the calculated moments around any point are in equilibrium, making the solution of the problem much easier.

Since the definition of work in mechanics is power times the displacement of the system in the direction of the force, the “d’Alembert principle” can also be expressed as the sum of the kinetic power and work functions that can be caused by all external forces as a result of any displacement of a system can be zero. This is particularly useful in the analysis of systems that satisfy some connection conditions, because forces that will not disrupt the connection will do absolutely no work. The law of conservation of energy and the variational formulation of mechanics also arise from the application of the total zero work principle, which applies to static problems, to dynamical problems, thanks to d’Alembert.

Prepared by: Sociologist Ömer Yıldırım

Source: Atatürk University Sociology Department 1st Year “Introduction to Philosophy” and 2nd, 3rd, 4th Grade “History of Philosophy” Lecture Notes (Ömer YILDIRIM)