Transient molecular electro-optics Cartesian rotation vector versus Eulerian angles.
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.
Evensen
Tom Richard
TR
Department of Physics, Norwegian University of Science and Technology (NTNU), Høgskoleringen 5, 7491 Trondheim, Norway.
Elgsaeter
Arnljot
A
Naess
Stine Nalum
SN
D000465:Algorithms; D004058:Diffusion; D004563:Electrochemistry / Q000379:methods*; D007700:Kinetics; D012399:Rotation