3. Virtual work and D’Alembert’s principle

One of the advantages of analytic mechanics is that it removes the need to deal with “internal forces”. Consider the problem of two masses attached by a rigid mass-less rod; in vector mechanics, one needs to know the tension in the rod to be able to write the forces on each mass and obtain the equation of motion. In principle, the rod itself is made of an almost infinite number of particles each exerting forces on each other, and a complete vectorial approach is not tractable. In analytic mechanics, we can distinguish “internal forces” and usually ignore them. Typically, these internal forces can be handled easily by using a constraint (e.g. the rod is a rigid object).

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