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• W2076015887 endingPage "54" @default.
• W2076015887 startingPage "35" @default.
• W2076015887 abstract "Euler angles (alpha,beta,gamma) are cumbersome from a computational point of view, and their link to experimental parameters is oblique. The angle-axis {Phi, n} parametrization, especially in the form of quaternions (or Euler-Rodrigues parameters), has served as the most promising alternative, and they have enjoyed considerable success in rf pulse design and optimization. We focus on the benefits of angle-axis parameters by considering a multipole operator expansion of the rotation operator D(Phi, n), and a Clebsch-Gordan expansion of the rotation matrices D(MM')(J)(Phi, n). Each of the coefficients in the Clebsch-Gordan expansion is proportional to the product of a spherical harmonic of the vector n specifying the axis of rotation, Y(lambdamu)(n), with a fixed function of the rotation angle Phi, a Gegenbauer polynomial C(2J-lambda)(lambda+1)(cosPhi/2). Several application examples demonstrate that this Clebsch-Gordan expansion gives easy and direct access to many of the parameters of experimental interest, including coherence order changes (isolated in the Clebsch-Gordan coefficients), and rotation angle (isolated in the Gegenbauer polynomials)." @default.
• W2076015887 created "2016-06-24" @default.
• W2076015887 creator A5038742663 @default.
• W2076015887 creator A5067287328 @default.
• W2076015887 creator A5068350068 @default.
• W2076015887 date "2007-02-01" @default.
• W2076015887 modified "2023-09-23" @default.
• W2076015887 title "Beyond Euler angles: Exploiting the angle–axis parametrization in a multipole expansion of the rotation operator" @default.
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• W2076015887 doi "https://doi.org/10.1016/j.ssnmr.2006.12.001" @default.
• W2076015887 hasPubMedId "https://pubmed.ncbi.nlm.nih.gov/17267183" @default.
• W2076015887 hasPublicationYear "2007" @default.
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