Abstract
An asymmetric top under the influence of time-dependent external forces is a rather complicated subject in mechanics. Efficient methods to describe the rotational motion are important as well in astrophysics as in molecular physics. The orientation of a rigid body relative to the laboratory system can be described by a rotation matrix. The equation of motion for the rotation matrix is derived. Different ways are discussed to parametrize the rotation matrix with a special focus on the representation by quaternions which is very efficient and avoids singularities inherent to the more common Euler angles. Methods to integrate the equations of motion are studied. Simple first- or second-order methods do not conserve orthogonality without special correction schemes. An implicit method avoids the loss of orthogonality. Computer experiments simulate a dipole rotating in a field and the collision of two rotating molecules.
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References
M.P. Allen, D.J. Tildesley, Computer Simulation of Liquids (Oxford University Press, 1989) ISBN 0-19-855645-4
R. Sonnenschein, A. Laaksonen, E. Clementi, J. Comput. Chem. 7, 645 (1986)
I.P. Omelyan, Phys. Rev. 58, 1169 (1998)
I.P. Omelyan, Comput. Phys. Comm. 109, 171 (1998)
H. Goldstein, Klassische Mechanik (Akademische Verlagsgesellschaft, Frankfurt a.Main, 1974)
I.P. Omelyan, Comput. Phys. 12, 97 (1998)
D.C. Rapaport, The Art of Molecular Dynamics Simulation. (Cambridge University Press, Cambridge, 2004) ISBN 0-521-44561-2.
T. Schlick, Molecular Modeling and Simulation (Springer, New York, NY, 2002) ISBN 0-387-95404-X
F. Schwabl, Statistical Mechanics (Springer, Berlin, 2003)
H. Risken, The Fokker-Planck Equation (Springer, Berlin Heidelberg, 1989)
E. Ising, Beitrag zur Theorie des Ferromagnetismus, Z. Phys. 31, 253–258 (1925). doi:10.1007/BF02980577
K. Binder, in “Ising model” Encyclopedia of Mathematics, Suppl. vol. 2, ed. by R. Hoksbergen (Kluwer, Dordrecht, 2000), pp. 279–281
L. Onsager, Phys. Rev. 65, 117 (1944)
B.M. McCoy, T.T. Wu, The Two-Dimensional Ising Model (Harvard University Press, Cambridge, MA, 1973) ISBN 0674914406
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Scherer, P.O. (2010). Rotational Motion. In: Computational Physics. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-13990-1_12
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DOI: https://doi.org/10.1007/978-3-642-13990-1_12
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