Louis Poinsot - Work

Work

"Poinsot was determined to publish only fully developed results and to present them with clarity and elegance. Consequently he left a rather limited body of work ..."

—Dictionary of Scientific Biography (see Sources)

Works include:

• Eléments de statique (1803)
• memoirs that dealt with the composition of moments and the composition of areas (1806)
• the general theory of equilibrium and of movements in systems (1806)
• polygons and polyhedra (1809)
• Theorie nouvelle de la rotation des corps (1834)

Poinsot was the inventor of geometrical mechanics, which showed how a system of forces acting on a rigid body could be resolved into a single force and a couple. Previous work done on the motion of a rigid body had been purely analytical with no visualization of the motion, and the great value of the work, as Poinsot says, it enables us to represent to ourselves the motion of a rigid body as clearly that as a moving point (Encyclopædia Britannica, 1911). In particular he devised, what is now known as, Poinsot's construction. This construction describes the motion of the angular velocity vector of a rigid body with one point fixed (usually its center of mass). He proved that the endpoint of the vector moves in a plane perpendicular to the angular momentum (in absolute space) of the rigid body.

He discovered four new regular polyhedra, in 1809, two of which appear in Kepler's work of 1619, although Poinsot was unaware of this. There are only four Kepler-Poinsot polyhedra, the other two are the great icosahedron and great dodecahedron, some people call these two the Poinsot solids. In 1810 Cauchy proved, using Poinsot's definition of regular, that the enumeration of regular polyhedra is complete. In 1990 a mistake was discovered in Poinsot's and Cauchy's definition when an internal inconsistency was discovered..

Poinsot worked on number theory studying Diophantine equations. However he is best known for his work in geometry and, together with Monge, regained geometry's leading role in mathematical research in France in the 19th century. Poinsot also contributed to the importance of geometry by creating a chair of advanced geometry at the Sorbonne in 1846. Poinsot created the chair for Chasles which he occupied until his death in 1880.