Introduzione


Abstract


En
An axiomatic approach to classical kinematics is developed. An affine four dimensional space E (event space), a three dimensional subspace(Error rendering LaTeX formula) (simultaneity space), an euclidean conformal metric G on(Error rendering LaTeX formula) and an orientation on T \equiv E_{/{\buildrel\_ \over S}} (time) constitute the general framework. The one-body absolute kinematics considers an absolute motion(Error rendering LaTeX formula), its absolute velocity DM:T → U and accelaration {D^2}M:T → {\buildrel\_ S}. The continum absolute kinematics considers a family of disjoint motions filling E and their velocities, accelerations and jacobians. A continum can be taken as a frame of reference, for it determines the position map p : E \rightarrow P. The set of position P is a C∈fty manifold, diffeomorphic to affine three dimensional spaces and endowed with a time depending metric g<sub>p</sub>: T \times TP \rightarrow \Re, a time depending affine connection Γ<sub>p</sub> : T \times {T^2}P \rightarrow \nu {T^2}P, a Coriolis map C<sub>P</sub>: T \times TP \rightarrow TP and a dragging map D<sub>P</sub>:T \times P \rightarrow TP. A classification of special frames considers affine, rigid, translating and inertial frames, characterized by the properties of their motions and their position spaces. The observed kinematics condiders the observed motion M<sub>P</sub> ≡ p · M, its velocity and acceleration and compares them with the absolute quantities. By comparison of observed kinematics, with respect to two frames, the addition velocities and generalized Coriolis theorem is obtained.

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