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On the foundations of ordinary and generalized rigid body dynamics and the principle of objectivity. (English) Zbl 1076.70002
Summary: This article presents the foundations of Newton-Euler rigid body dynamics and its generalized forms in the light of the objectivity principle. We prove that most of the features of dynamics may be directly deduced from this principle and from properties of the group defining the geometry. In particular, these deductions seem to close the conjectures about the relevance of the objectivity principle to dynamics.

70E15 Free motion of a rigid body
70G45 Differential geometric methods (tensors, connections, symplectic, Poisson, contact, Riemannian, nonholonomic, etc.) for problems in mechanics
70G65 Symmetries, Lie group and Lie algebra methods for problems in mechanics