How can d’Alembert’s principle turn a dynamics problem into a statics problem?

Jean Le Rond d’Alembert’s principle transforms a dynamics problem into a statics problem by introducing a fictitious force, often called an inertial force or reversed effective force.1

While Newton’s second law of motion defines the relationship between force ($F$), mass ($m$), and acceleration ($a$) as $F=ma$, d’Alembert’s principle rearranges this into the form $F-ma=0$. By treating the negative of the mass times acceleration ($-ma$) as an additional force acting on the body, the system is brought into a state of equilibrium.12

This approach simplifies complex analyses, such as calculating stress in machine components, because it is mathematically easier to determine unknown forces on bodies in equilibrium than on those in motion. By applying this principle, engineers can analyze moving parts as if they were stationary, provided they account for the inertial forces acting upon them.1