The Principle of Virtual Velocities

From Lagrange’s Méchanique analytique onwards, the principle of virtual velocities, or displacements, became a cornerstone of the whole mechanics. It was proposed with slightly different interpretations by several mathematicians between the end of the eighteenth and the first half of the nineteenth century. Chasles dedicated some reflections to this principle, although he did not develop a complex work like those on the displacement of a rigid body and on the system of forces. I prove that his contributions to the deduction and interpretation of the principle of virtual velocities belong to the development of his foundational programme. I argue for such thesis in the second section. The first section is, instead, dedicated to the contributions of the mathematicians who preceded Chasles. This is paramount to appreciate the homologies and the differences between his approach and those proposed by the other scholars. The Conclusion follows.