References

1

J.A. Schouten, Ricci-Calculus. An Introduction to tensor analysis and its geometrical applications (Springer-Verlag, Berlin, 1954).

2

V.I. Arnold, V.V. Koslov and A.I. Neishtadt, in: Encyclopedia of Mathematical Sciences, Dynamical Systems III, Mathematical Aspects of Classical and Celestial Mechanics (Springer-Verlag, Berlin, 1988);
L.A. Pars, A Treatise on Analytical Dynamics (Heinemann, London, 1965);
G. Hamel, Theoretische Mechanik - Eine einheitliche Einführung in die gesamte Mechanik, Springer Series in Mathematics, Vol. 57 (Springer, Berlin, 1978).

3

L.S. Polak (ed.), Variational principles of mechanics. Collection of papers (Moscow, Fizmatgiz, 1959).

4

see, e.g., C.W. Misner, K.S. Thorn and J.A. Wheeler, Gravitation (New York, W.H. Freeman and Co, 1973) and references therein.

5

Autoparallels as trajectories of spinless test particles were proposed in
V.N. Ponomorev, Observable effects of torsion in space-time, Preprint of the Warsaw University (February 1971).
This was criticized on the basis of a general class of gravitational field theories with torsion:
F.W. Hehl, Phys. Lett. A 36, 225 (1971).
Recently, however, the analogy of torsion with dislocations in crystals has produced more arguments in favor of autoparallel trajectories:
H. Kleinert, Path Integrals in Quantum Mechanics, Statistics and Polymer Physics (World Scientific, Singapore, Second Edition, 1995);
H. Kleinert, Gauge Fields in Condensed Matter, Vol. II, Stresses and Defects (World Scientific, Singapore, 1989). See in particular pp. 1338-1377;
P. Fiziev and H. Kleinert, Europhys. Lett. 35, 241 (1996) (hep-th/9503074);
H. Kleinert and A. Pelster, Berlin preprint (1996) (gr-qc/9605028);
H. Kleinert, FU-Berlin preprint (1997) (APS E-Print aps1997sep03 002).

6

T.W. Kibble, J.Math.Phys. 2 (1961) 212.

7

P.A.M. Dirac, Lectures on Quantum Mechanics (Yeshiva University Press, NY, 1964).