Volume 17: Pages 526-535, 2004
On the Concepts of Frame of Reference and Connection in Space‐Time Bundles of Classical Mechanics
Dipartimento di Matematica dell'Università di Parma, Via D'Azeglio, 85‐43100, Parma, Italy
The definition of frame of reference in classical space‐time bundles is investigated in the general case of bundles whose fibers are not Euclidean and of frames without the rigidity requirement. The enrichment of the geometry of the bundle following from the presence of a frame of reference, viewed as a particular time‐like vector field, is analyzed. Space‐like tensor fields, unless totally contravariant, are proved to be correctly defined only if a frame of reference H is assigned. The connection associated with H is introduced and the selection of special covariant and time derivatives associated with H is soundly motivated. The usual kinematic quantities relative to H are defined. The relationships between pairs of frames are examined and the concepts of relative rigidity, relative spin, and relative acceleration are defined and investigated. The main results of relative kinematics are shown to fit readily into this geometric context.
Keywords: classical space‐time, frame of reference, connection
Received: June 15, 2004; Published Online: December 15, 2008