A geometric setting for classical molecular dynamics
Annales de l'I.H.P. Physique théorique, Tome 47 (1987) no. 2, pp. 199-219. 
@article{AIHPA_1987__47_2_199_0,
     author = {Iwai, Toshihiro},
     title = {A geometric setting for classical molecular dynamics},
     journal = {Annales de l'I.H.P. Physique th\'eorique},
     pages = {199--219},
     publisher = {Gauthier-Villars},
     volume = {47},
     number = {2},
     year = {1987},
     mrnumber = {921313},
     zbl = {0655.58041},
     language = {en},
     url = {http://www.numdam.org/item/AIHPA_1987__47_2_199_0/}
}
TY  - JOUR
AU  - Iwai, Toshihiro
TI  - A geometric setting for classical molecular dynamics
JO  - Annales de l'I.H.P. Physique théorique
PY  - 1987
SP  - 199
EP  - 219
VL  - 47
IS  - 2
PB  - Gauthier-Villars
UR  - http://www.numdam.org/item/AIHPA_1987__47_2_199_0/
LA  - en
ID  - AIHPA_1987__47_2_199_0
ER  - 
%0 Journal Article
%A Iwai, Toshihiro
%T A geometric setting for classical molecular dynamics
%J Annales de l'I.H.P. Physique théorique
%D 1987
%P 199-219
%V 47
%N 2
%I Gauthier-Villars
%U http://www.numdam.org/item/AIHPA_1987__47_2_199_0/
%G en
%F AIHPA_1987__47_2_199_0
Iwai, Toshihiro. A geometric setting for classical molecular dynamics. Annales de l'I.H.P. Physique théorique, Tome 47 (1987) no. 2, pp. 199-219. http://www.numdam.org/item/AIHPA_1987__47_2_199_0/

[1] C. Eckart, Some studies concerning rotating axes and polyatomic molecules. Phys. Rev., t. 47, 1935, p. 552-558. | Zbl

[2] J.D. Louck and H.W. Galbraith, Eckart vectors, Eckart frames, and polyatomic molecules. Rev. Mod. Phys., t. 48, 1976, p. 69-106. | MR

[3] B.T. Sutcliffe, The Eckart Hamiltonian for molecules, A critical exposition, in The Quantum Dynamics of Molecules, ed. by R. G. Woolley, NATO ASI Ser. Plenum, New York, 1980.

[4] A. Guichardet, On rotation and vibration motions of molecules. Ann. Inst. Henri Poincaré, t. 40, 1984, p. 329-342. | Numdam | MR | Zbl

[5] J. Marsden and W. Weinstein, Reduction of symplectic manifolds with symmetry. Rep. Math. Phys., t. 5, 1974, p. 121-130. | MR | Zbl

[6] S. Sternberg, Lectures on Differential Geometry, Prentice-Hall, Englewood Cliffs, NJ, 1964. | MR | Zbl

[7] S. Kobayashi and K. Nomizu, Foundations of Differential Geometry, vol. I, Interscience Publishers, New York, 1963. | MR | Zbl

[8] D. Bleecker, Gauge Theory and Variational Principles, Addison-Wesley, Reading, MA, 1981. | MR | Zbl

[9] C. Nash and S. Sen, Topology and Geometry for Physicists, Academic Press, New York, 1983. | MR | Zbl

[10] T. Eguchi, P.B. Gilkey and A.J. Hanson, Gravitation, gauge theories and differential geometry, Physics Reports, t. 66, No. 6, 1980. | MR

[11] V.I. Arnold, Mathematical Methods of Classical Mechanics. Springer-Verlag, New York, 1978. | MR | Zbl

[12] R. Abraham and J.E. Marsden, Foundations of Mechanics, Benjamin/Cummings. Reading. MA, 1978. | MR | Zbl

[13] V. Guillemin and S. Sternberg, Symplectic Techniques in Physics. Cambridge Univ. Press, Cambridge, 1984. | MR | Zbl

[14] E.B. Wilson, Jr., J.C. Decius and P.C. Cross, Molecular Vibrations. McGraw Hill, New York, 1955.

[15] T. Iwai, A gauge theory for the quantum planar three-body problem. J. Math. Phys., t. 28, 1987, p. 964-974. | MR | Zbl

[16] T. Iwai, A geometric setting for internal motions of the quantum three-body system. J. Math. Phys., t. 28, 1987, p. 1315-1326. | MR

[17] Y. Matsushima, Differentiable Manifolds, Marcel Dekker, New York, 1972. | MR | Zbl

[18] S. Male, Topology and mechanics. I, Invent. Math., t. 10, 1970, p. 305-331. | MR | Zbl

[19] J.E. Marsden, Lectures on Geometric Methods in Mathematical Physics. Society for Industrial and Applied Mathematics, Philadelphia, PA, 1981. | MR | Zbl

[20] A. Wintner, The Analytical Foundations of Celestial Mechanics. Princeton Univ. Press, Princeton, NJ, 1941. | MR | Zbl

[21] M. Kummer, On the construction of the reduced space of a Hamiltonian system with symmetry. Indiana Univ. Math. J., t. 30, 1981, p. 281-291. | MR | Zbl

[22] R. Montgomery, The structure of reduced cotangent phase space for nonfree group actions. Preprint, Univ. of Calif., Berkeley, PAM-143, 1983.

[23] L. Bos and M.J. Gotay, Reduced canonical formalism for a particle with zero angular momentum, in 13th Internat. Colloq. on Group Theoret. Methods in Physics, ed. by W. W. ZACHARY, World Scientific, Singapore, 1984, p. 83-91. | MR | Zbl

[24] S. Smale, Topology and mechanics. II, Invent. Math., t. 11, 1970, p. 45-64. See also [12], Chap. 10. | MR | Zbl

[25] A. Tachibana and T. Iwai, Complete molecular Hamiltonian based on the Born-Oppenheimer adiabatic approximation, Phys. Rev., t. A33, p. 2262-2269.