Building bodies: Euler and impressed force mechanics

Abstract

Abstract During the early decades of the 18th century, theorists working in rational mechanics came to terms with the insufficiency of Newton’s laws for treating the motions of extended bodies. After the 1730s, rational mechanics learned how to tackle the motion of extended bodies with internal constraints, such as rigidity and incompressibility. In Chapter 10, the authors investigate these developments in relation to the problem of bodies. The greatest advances were due to the Bernoullis, d’Alembert, and especially Euler. These figures relied on a dual idea: constraints are due to internal forces; and the balance laws for impressed external forces govern the actions of internal constraints as well. The upshot was a broad-scope mechanics in a specific formulation, due to Euler. The authors make clear the successes and limitations of Euler’s achievements, with respect to the problem of bodies.