Transient molecular electro-optics Cartesian rotation vector versus Eulerian angles |
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Authors: | Evensen Tom Richard Elgsaeter Arnljot Naess Stine Nalum |
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Institution: | aDepartment of Physics, Norwegian University of Science and Technology (NTNU), Høgskoleringen 5, 7491 Trondheim, Norway |
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Abstract: | Comparing the Euler angles, the classical choice of generalized coordinates describing the three rotational degrees of freedom of a rigid body, and the Cartesian rotation vector, we show that they both have their advantages and disadvantages in kinetic theory and Brownian dynamics analysis of molecular electro-optics. The Eulerian angles often yield relatively simple, yet singular, equations of motion, while their counterparts expressed in terms of Cartesian rotation vector are non-singular but more complex. In a special case, we show that the generalized force associated with the Cartesian rotation vector equals the torque. In addition, we introduce a new graphical approach to qualitatively track how changes in the Eulerian angles affect the Cartesian rotation vector. |
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Keywords: | Molecular electro-optics Cartesian rotation vector Eulerian angles Brownian dynamics Theory |
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