| Autor: |
Manfred Trümper |
| Rok vydání: |
1983 |
| Předmět: |
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| Zdroj: |
Annals of Physics. 149:203-233 |
| ISSN: |
0003-4916 |
| DOI: |
10.1016/0003-4916(83)90305-6 |
| Popis: |
Holonomic rheonomic systems having a finite number of degrees of freedom are considered in classical nonrelativistic mechanics. It is shown that the configuration spacetime manifold M of such a system can be furnished with a linear symmetric connection (called the “dynamical connection”) in such a way that the worldline of the system is a geodesic on M . The connection is based upon a degenerate metric structure (called a “generalized Galilei structure”) which in turn is uniquely determined by the system and the forces acting on it. The connection is compatible with the generalized Galilei structure in the sense that the covariant derivatives of the latter vanish. Systems which can be described in terms of a Lagrangian give rise to a particularly interesting class of dynamical connections, called “Lagrange connections,” whose geometry is studied in some detail. Within the class of generalized Galilei connections they are characterized by a geometrical condition imposed on the affine curvature tensor. Noether symmetries of the dynamical system turn out to be equivalent to “isometries” of the generalized Galilei structure together with collineations of the Lagrange connection. They form a Lie group. Spacelike generators of Noether symmetries are linked to the existence of “conservors” (i.e., covectors with vanishing symmetrized covariant derivatives). Timelike generators of Noether symmetries give rise to (second rank) Killing tensors. |
| Databáze: |
OpenAIRE |
| Externí odkaz: |
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