D’Alembert’s principle states that for a system of mass of particles, the sum of difference of the force acting on the system and the time derivatives of the momenta is zero when projected onto any virtual displacement. It is also known as Lagrange-d’Alembert principle, named after French mathematician and physicist Jean le Rond d’Alembert.
D’Alembert’s principle can be explained mathematically in following way:
i: integral used for the identification of variable corresponding to particular particle in the system
Fi: total applied force on the ith place
mi: mass of the ith particles
ai: acceleration of ith particles
miai: time derivative representation
𝜹ri: virtual displacement of ith particle