Chasles' theorem

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Several results in mathematics have been attributed to Michel Chasles and named Chasles' theorem:

• In kinematics, any motion of a rigid body can be decomposed into a translation followed or preceded by a rotation. The translation may be found as the vector difference between the centroids of the positions of the body prior to and after the motion, while any motion that preserves the centroid is a rotation around the centroid (Kumar).

• In gravitation, the Newtonian gravitational attraction of a spherical shell, outside of that shell, is equivalent mathematically to the attraction of a point mass (Peirce 1855).

• 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 (Weisstein).

[edit] References

• Kumar, V.. MEAM 520 notes: The theorems of Euler and Chasles.
• M. Chasles. (1830). "Note sur les proprietes generales du systeme de deux corps semblables entr’eux et places d’une maniere quelconque dans l’espace; et sur le deplacement fini ou infiniment petit d’un corps solide libre". Bulletin des Sciences Mathematiques, Astronomiques, Physiques et Chimiques 14: 321–326.

• Peirce, Benjamin (1855). A System of Analytic Mechanics, 104.

• Weisstein, Eric W., Chasles's Theorem at MathWorld.