Chasles' theorem

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Several results in mathematics have been attributed to Michel Chasles (1793–1880) and named Chasles' theorem:

  • In kinematics, the most general rigid body displacement can be produced by a translation along a line (called its screw axis) followed (or preceded) by a rotation about that line.[1][2]
  • In gravitation, the Newtonian gravitational attraction of a spherical shell, outside of that shell, is equivalent mathematically to the attraction of a point mass.[3]
  • In algebraic geometry, if two pencils of curves have no curves in common, then the intersections of those curves forms another pencil of curves the degree of which can be calculated from the degrees of the initial two pencils.[4]


References

  1. ↑ Kumar, V. "MEAM 520 notes: The theorems of Euler and Chasles". 
  2. ↑ William B. Heard (2006) Rigid Body Mechanics, page 42, Wiley-VCH ISBN 3-527-40620-4
  3. ↑ Peirce, Benjamin (1855). A System of Analytic Mechanics. p. 104. 
  4. ↑ Weisstein, Eric W., "Chasles's Theorem", MathWorld.
  • M. Chasles. (1830). "Note sur les propriétés générales du système de deux corps semblables entr'eux et placés d'une manière quelconque dans l'espace; et sur le déplacement fini ou infiniment petit d'un corps solide libre.". Bulletin des Sciences Mathematiques, Astronomiques, Physiques et Chimiques 14: 321–326.  (Notes on the general properties of a system of 2 identical bodies randomly located in space; and on the finite or infinitesimal motion of a free solid body.)



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