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Parametrization of an orthogonal matrix in terms of generalized eulerian angles
Author(s) -
Raffenetti Richard C.,
Ruedenberg Klaus
Publication year - 2009
Publication title -
international journal of quantum chemistry
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.484
H-Index - 105
eISSN - 1097-461X
pISSN - 0020-7608
DOI - 10.1002/qua.560040725
Subject(s) - parametrization (atmospheric modeling) , eulerian path , matrix (chemical analysis) , character (mathematics) , orthogonal matrix , mathematics , physics , mathematical analysis , classical mechanics , geometry , quantum mechanics , orthogonal basis , chemistry , lagrangian , chromatography , radiative transfer
Formulas are derived which express an arbitrary orthogonal matrix T in terms of N(N ‐ 1)/2 independent parameters γ pq ( p = 1, 2, …, N ; q = 1, 2, …, N ; p < q ). The parameters have angular character and can be considered as generalized Eulerian angles in N dimensions. Expressions for the first derivatives of the matrix elements T ij with respect to these parameters are also given. Practical applications, in particular for variational problems, are discussed.