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Literatur
G. H. Katzin andJ. Levine:Journ. Math. Phys.,9, 8 (1968).
G. H. Katzin andJ. Levine:Colloquium Mathematicum (Wroclaw),26, 21 (1972).
G. H. Katzin:Journ. Math. Phys.,14 (1973), to appear.
The symbol D/dt indicates absolute differentiation with respect to the Christoffel symbols based upon the metric tensorg ij of the configuration spaceV n . Lower–case Latin indices range from 1 ton. Summation notation is used throughout.V(x) is the potential energy. Partial differentiation is indicated by a comma (,).
See for exampleC. W. Kilmister:Hamiltonian Dynamics (New York, 1965).
Upper–case Latin indices range from 1 to 2n.
The conditions for trajectory collineations of a conservative dynamical system were formulated in a similar manner in the configuration space formulation. Refer to ref. (3).G. H. Katzin:Journ. Math. Phys.,14 (1973), to appear.
K. Yano:The Theory of Lie Derivatives and Its Application (Amsterdam, 1957).
This theorem is the phase–space version of the related integral theorem. Refer to ref. (3)G. H. Katzin:Journ. Math. Phys.,14 (1973), to appear.
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Katzin, G.H. The related integral theorem in phase space: A generalization of Poisson’ theorem on constants of the motion. Lett. Nuovo Cimento 7, 213–216 (1973). https://doi.org/10.1007/BF02727415
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DOI: https://doi.org/10.1007/BF02727415