Journal of Physical Studies 3(1), 1–11 (1999) DOI: https://doi.org/10.30970/jps.03.1 NON-POINT TRANSFORMATIONS IN CLASSICAL MECHANICS

R. P. Gaida

Editorial Note.
This paper by the late Professor Gaida (1928-1998) was available only as Preprint of the Institute for Condensed Matter Physics (ICMP-94-5E, Lviv, 1994). We publish this paper on the basis of the preprint text taking into account some corrections contained in the typed manuscript from the archives of Professor Gaida.

Institute for Condensed Matter Physics of the National Academy of Sciences of Ukraine
1 Svientsitskyi Str., Lviv, UA-290011, Ukraine

The problem of applicability of the non–point transformations in the Lagrangian and Newtonian formalism of classical mechanics is investigated. These transformations correspond to non–point canonical transformations and belong to the class of transformations tangent to a given system of second–order differential equations. The methods for constructing such transformations are considered. Two theorems concerning non–point transformations in Hamilton's variational principle and connection between transformed and initial Lagrangians are proved. The relation of the results to canonical transformations in Hamiltonian formalism is discussed. The general results are illustrated by a simple example.

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