Classical Physics

0805 Submissions

[2] viXra:0805.0004 [pdf] submitted on 12 May 2008

Helmholtz’s Decomposition Theorem, Etc.

Authors: R. I. Khrapko
Comments: recovered from

The fact is used that electromagnetic fields are covariant (antisymmetric) tensors or contravariant (antisymmetric) tensor densities, which are mutual conjugated. The conjugation allows many-fold specific differentiation of the fields and leads to field chains. An integral operation, named the generation, is considered, which is reverse to the specific differentiation. The double generation yields zero as well as the double differentiation. The Helmholtz decomposition is compared with the Poincare decomposition, and many ways of the Helmholtz decomposition are presented. Laplace operator and the inverse Laplace operator are expressed in terms of the differential and integral operations. All results are illustrated by simple examples.
Category: Classical Physics

[1] viXra:0805.0003 [pdf] submitted on 12 May 2008

A Manifest Failure of Grassmann’s Force

Authors: Jorge Guala-Valverde, Ricardo Achilles
Comments: recovered from

The growing interest in a thorough revision of the tenets of classical electrodynamics [1,2] compels us to reconsider the torque-production mechanism presently applied to homopolar machines founded – indistinctively – on Ampére or Grassmann’s basis. Recent crucial experimentation [1] definitively rules out the latter rationale for its physical inconsistency.
Category: Classical Physics