Editing D'Alembert's principle (section)

==D'Alembert's principle of inertial forces==
D'Alembert showed that one can transform an accelerating rigid body into an equivalent static system by adding the so-called "[[inertial force]]"  and "inertial torque" or moment. The inertial force must act through the center of mass and the inertial torque can act anywhere. The system can then be analyzed exactly as a static system subjected to this "inertial force and moment" and the external forces. The advantage is that in the equivalent static system one can take moments about any point (not just the center of mass). This often leads to simpler calculations because any force (in turn) can be eliminated from the moment equations by choosing the appropriate point about which to apply the moment equation (sum of moments = zero). Even in the course of Fundamentals of Dynamics and Kinematics of machines, this principle helps in analyzing the forces that act on a link of a mechanism when it is in motion. In textbooks of engineering dynamics, this is sometimes referred to as ''d'Alembert's principle''. 

Some educators caution that attempts to use d'Alembert inertial mechanics lead students to make frequent sign errors.<ref name=":0">[https://www.engineering.cornell.edu/faculty-directory/andy-ruina Ruina, Andy L.], and [[Rudra Pratap]]. [http://ruina.tam.cornell.edu/Book/ Introduction to statics and dynamics]. Pre-print for Oxford University Press, 2008.</ref> A potential cause for these errors is the sign of the [[Inertial Force|inertial forces]]. Inertial forces can be used to describe an apparent force in a [[non-inertial reference frame]] that has an acceleration <math>\mathbf{a}</math> with respect to an [[inertial reference frame]]. In such a non-inertial reference frame, a mass that is at rest and has zero acceleration in an inertial reference system, because no forces are acting on it, will still have an acceleration <math>-\mathbf{a}</math> and an apparent inertial, or pseudo or [[fictitious force]] <math>-m\mathbf{a}</math> will seem to act on it: in this situation the inertial force has a minus sign.<ref name=":0" />