D’Alembert’s Principle of Virtual Work - Active Forces and Workless Constraint Forces

Explore D'Alembert's Principle of Virtual Work in this comprehensive lecture on analytical dynamics. Delve into nonholonomic constraints, focusing on rolling without slipping, before examining the core concept of virtual work. Learn how forces are decomposed into constraint and active forces, and understand the significance of virtual admissible displacements. Discover how workless constraints lead to equations of motion containing only active forces, forming the basis of D'Alembert's Principle. Apply this principle to a single-particle pendulum system and extend it to multi-particle systems. Gain valuable insights into advanced dynamics concepts essential for engineering and physics applications.

Nonholonomic constraints, in particular rolling without slipping.
D’Alembert’s Principle of Virtual Work..
Virtual work is the concept of the work done by the forces in moving them through an admissible virtual displacement. The constraint forces do no work, and so are called "workless constraints". .
When we project Newton's 2nd Law into the admissible virtual displacement directions , we get some equations of motion which do not contain the constraint forces, only the active forces along the directions in which motion is possible. This is what gives rise to D’Alembert’s Principle of Virtual Work..
We demonstrate this example on the pendulum, a single particle system, and then .
formulate D’Alembert’s Principle of Virtual Work for a multiparticle system .