@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/} }
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] Some studies concerning rotating axes and polyatomic molecules. Phys. Rev., t. 47, 1935, p. 552-558. | Zbl
,[2] Eckart vectors, Eckart frames, and polyatomic molecules. Rev. Mod. Phys., t. 48, 1976, p. 69-106. | MR
and ,[3] 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] On rotation and vibration motions of molecules. Ann. Inst. Henri Poincaré, t. 40, 1984, p. 329-342. | Numdam | MR | Zbl
,[5] Reduction of symplectic manifolds with symmetry. Rep. Math. Phys., t. 5, 1974, p. 121-130. | MR | Zbl
and ,[6] Lectures on Differential Geometry, Prentice-Hall, Englewood Cliffs, NJ, 1964. | MR | Zbl
,[7] Foundations of Differential Geometry, vol. I, Interscience Publishers, New York, 1963. | MR | Zbl
and ,[8] Gauge Theory and Variational Principles, Addison-Wesley, Reading, MA, 1981. | MR | Zbl
,[9] Topology and Geometry for Physicists, Academic Press, New York, 1983. | MR | Zbl
and ,[10] Gravitation, gauge theories and differential geometry, Physics Reports, t. 66, No. 6, 1980. | MR
, and ,[11] Mathematical Methods of Classical Mechanics. Springer-Verlag, New York, 1978. | MR | Zbl
,[12] Foundations of Mechanics, Benjamin/Cummings. Reading. MA, 1978. | MR | Zbl
and ,[13] Symplectic Techniques in Physics. Cambridge Univ. Press, Cambridge, 1984. | MR | Zbl
and ,[14] Molecular Vibrations. McGraw Hill, New York, 1955.
, and ,[15] A gauge theory for the quantum planar three-body problem. J. Math. Phys., t. 28, 1987, p. 964-974. | MR | Zbl
,[16] A geometric setting for internal motions of the quantum three-body system. J. Math. Phys., t. 28, 1987, p. 1315-1326. | MR
,[17] Differentiable Manifolds, Marcel Dekker, New York, 1972. | MR | Zbl
,[18] Topology and mechanics. I, Invent. Math., t. 10, 1970, p. 305-331. | MR | Zbl
,[19] Lectures on Geometric Methods in Mathematical Physics. Society for Industrial and Applied Mathematics, Philadelphia, PA, 1981. | MR | Zbl
,[20] The Analytical Foundations of Celestial Mechanics. Princeton Univ. Press, Princeton, NJ, 1941. | MR | Zbl
,[21] 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] The structure of reduced cotangent phase space for nonfree group actions. Preprint, Univ. of Calif., Berkeley, PAM-143, 1983.
,[23] 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
and ,[24] Topology and mechanics. II, Invent. Math., t. 11, 1970, p. 45-64. See also [12], Chap. 10. | MR | Zbl
,[25] Complete molecular Hamiltonian based on the Born-Oppenheimer adiabatic approximation, Phys. Rev., t. A33, p. 2262-2269.
and ,