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### 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 $DM:T â†’ U$ and accelaration ${D^2}M:T â†’ {\buildrel\_ S}$. 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 Câˆˆfty manifold, diffeomorphic to affine three dimensional spaces and endowed with a time depending metric $gp: T \times TP \rightarrow \Re$, a time depending affine connection $Î“p : T \times {T^2}P \rightarrow \nu {T^2}P$, a Coriolis map $CP: T \times TP \rightarrow TP$ and a dragging map $DP:T \times P \rightarrow TP$. 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 $MP â‰¡ p Â· M$, 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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