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On the variational formulation of systems with non‐holonomic constraints
Author(s) -
Delphenich D.H.
Publication year - 2009
Publication title -
annalen der physik
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.009
H-Index - 68
eISSN - 1521-3889
pISSN - 0003-3804
DOI - 10.1002/andp.200910364
Subject(s) - cosmic microwave background , physics , planck , photon , intensity (physics) , boundary (topology) , quantum electrodynamics , astrophysics , quantum mechanics , mathematical analysis , mathematics , anisotropy
In a previous article by the author, it was shown that one could effectively give a variational formulation to non‐conservative mechanical systems by starting with the first variation functional instead of an action functional. In this article, it is shown that this same approach will also allow one to give a variational formulation to systems with non‐holonomic constraints. The key is to use an adapted anholonomic local frame field in the formulation, which then implies the replacement of ordinary derivatives with covariant ones. The method is then applied to the case of a vertical disc rolling without slipping or friction on a plane.