Parametrization of an orthogonal matrix in terms of generalized eulerian angles
Richard Charles Raffenetti, Klaus Ruedenberg · International Journal of Quantum Chemistry · 2009
Formulas are derived which express an arbitrary orthogonal matrix T in terms of N(N - 1)/2 independent parameters γpq (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 Tij with respect to these parameters are also given. Practical applications, in particular for variational problems, are discussed.