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16 - Mechanics in Newton’s Wake

from Part II - Disciplinary Activities

Published online by Cambridge University Press:  14 January 2022

David Marshall Miller
Affiliation:
Iowa State University
Dana Jalobeanu
Affiliation:
University of Bucharest
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Summary

Newton’s remarkable achievements in planetary theory and dynamics were followed by a century of equally remarkable advances in the generalized science of forces acting on bodies in motion. Far from merelyformalizing the Newtonian framework, these advances aimed at solving deep problems left in Newton’s wake. First, Newtonian theory focused on centripetal forces, which are not characteristic of motion under arbitrary constraints or bodily deformation due to pressure and stress. Second, Newton’s attempts at fluid mechanics made clear that media could not be adequately analyzed using strategies developed for point-particles. Both considerations suggested that different forms of body required different analytical and conceptual tools. They required the formulation of generalized principles flexible enough to treat heterogeneous material configurations, but stringent enough to preserve the unity of mechanics as a study of matter and motion. Ultimately, Newton’s successors established a new discipline, analytical mechanics. Its primary object of investigation was the functional representation of the invariant relations behind dynamic phenomena, not the geometric representation of trajectories. The philosophical suppositions behind the new mechanics constituted a new mechanical philosophy, but one that hearkened back to, and completed the project of, the mechanical philosophy of the mid-seventeenth century.

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Publisher: Cambridge University Press
Print publication year: 2022

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