Mechanics, mathematical physics and foundations of mathematics in the 18th and 19th Centuries

# seminar: On the Origin of Vector Calculus in Geometry and Mechanics

speaker: Sandro Caparrini (Dipartimento di Matematica della Università di Torino)

abstract: The concept of energy in mechanics is significant because of some mathematical theorems, today reported in every textbook. Mainly, it leads to a first integration of the equations of motion. We look for the origin of these theorems and for their exact formulation. Apparently, the first non-trivial applications of a rudimentary energy principle appear in the work of Huygens (1684). Newton obtained the relation between work and kinetic energy by means of a semi-geometrical reasoning (1687); his result was put into a purely analytical form by Varignon (1700). Johann I Bernoulli thoroughly discussed the conservation of kinetic energy in his Discours sur les loix de la communication du mouvement (1727), and Daniel Bernoulli applied the general principle to fluid mechanics (1738). D’Alembert derived the conservation of kinetic energy during impact from his principle of dynamics (1743). The first general statement and proof of the conservation of energy for a system of mass-points were perhaps given by Lagrange (1780).

timetable:
Tue 8 Jul, 10:15 - 10:55, Aula Bianchi Scienze
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