Herglotz-Noether theorem

The Herglotz-Noether theorem in special relativity, named after Gustav Herglotz and Fritz Noether, restricts the possible linear and rotational motions of a Born-rigid object.[1][2] It was pointed out that the motion of the whole rigid body is in general definitely determined by the arbitrarily defined motion of a single point of it. (According to Herglotz, exceptions only take place when the world-lines have constant curvature.) In consequence, a Born rigid body only has three degrees of freedom.[3]

A more recent expression of the Herglotz-Noether theorem states, that rotational rigid motion in Minkowski space must be a Killing motion.[4]

References

  1. ↑ Herglotz, Gustav (1909), "Über den vom Standpunkt des Relativitätsprinzips aus als starr zu bezeichnenden Körper" [On bodies that are to be designated as "rigid" from the standpoint of the relativity principle], Annalen der Physik, 336 (2): 393–415, doi:10.1002/andp.19103360208
  2. ↑ Noether, Fritz (1910). "Zur Kinematik des starren Körpers in der Relativtheorie". Annalen der Physik. 336 (5): 919–944. Bibcode:1910AnP...336..919N. doi:10.1002/andp.19103360504.
  3. ↑ Pauli, Wolfgang (1981) [1921]. Theory of Relativity. New York: Dover. ISBN 0-486-64152-X.
  4. ↑ Giulini, Domenico (2008). "The Rich Structure of Minkowski Space". Minkowski Spacetime: A Hundred Years Later. Fundamental Theories of Physics. 165. Springer. p. 83. arXiv:0802.4345Freely accessible. ISBN 978-90-481-3474-8.
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