Geodesic
Rotation of supermolecules around an intermediate axis of inertia
Vestnik Tomskogo gosudarstvennogo universiteta. Matematika i mehanika, no. 80 (2022), pp. 49-58 Cet article a éte moissonné depuis la source Math-Net.Ru

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In the problem of the inertial rotation of molecular objects, only kinematic relations for the nodes of the molecular structure are evolutionary. These relations determine the position of the atoms of a supermolecule depending on the instantaneous angular velocity of the object in inertial motion. All other relations are algebraic, since they are integrals of the equations of rotational motion. The latter relations include both the projections of the angular velocities of the molecule and the instantaneous coordinates of the atoms. Within the framework of the fourth-order Runge-Kutta scheme, each time step is divided into four positions. Initially, in each of these positions, new values of coordinates are determined or the initial coordinates of atoms at the first position of the first time step are used. After the coordinates are found, in the same position, the projections of angular velocities of the supermolecule are obtained from conservation relations for the projections of the angular momentum. Based on the values of the coordinates in four positions, the coordinates on a new time layer are recalculated. After that, solving the system of three linear algebraic equations according to Cramer's rule, the projections of angular velocities at a new time step are determined. Then, the cycle is repeated. During the inertial rotation, the kinetic energy of an object is conserved. Verification of the calculated kinetic energy shows that the result is obtained with machine accuracy. Further, the constructed calculation scheme is used to study the Louis Poinsot instability. The full range of the considered instability for a fullerene C$_{100}$ (C$_{1}$ symmetry) is presented.
Keywords: numerical modeling, molecular dynamics, fullerenes. 
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     title = {Rotation of supermolecules around an intermediate axis of inertia},
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M. A. Bubenchikov; D. V. Mamontov; S. A. Azheev; A. A. Azheev. Rotation of supermolecules around an intermediate axis of inertia. Vestnik Tomskogo gosudarstvennogo universiteta. Matematika i mehanika, no. 80 (2022), pp. 49-58. http://geodesic.mathdoc.fr/item/VTGU_2022_80_a4/

[1] Goldstein H., Classical Mechanics, 2nd ed., Addison-Wesle, USA, 1980, 638 pp. | MR

[2] Bubenchikov M. A., Bubenchikov A. M., Mamontov D. V., “Vrascheniya i vibratsii torov v mole kulyarnom komplekse C20@C80”, Vestnik Tomskogo gosudarstvennogo universiteta. Matematika i mekhanika, 2021, no. 71, 35–48 | DOI | MR

[3] Bubenchikov M. A., Bubenchikov A. M., Mamontov D. V., Kaparulin D. S., Lun-Fu A. V., “Vraschenie torov v strukture zhidkogo kristalla”, Vestnik Tomskogo gosudarstvennogo universiteta. Matematika i mekhanika, 2021, no. 73, 42–49 | DOI

[4] Bubenchikov A. M., Bubenchikov M. A., Mamontov D. V., Kaparulin D. S., Lun-Fu A. V., “Dynamic state of columnar structures formed on the basis of carbon nanotori”, Fullerenes, Nanotubes and Carbon Nanostructures, 29:10 (2021), 1–7 | DOI

[5] Lun-Fu A.V., Bubenchikov M. A., Bubenchikov A. M., Mamontov D. V., Borodin V. A., “Interaction of molecular tori in columnar structures”, Journal of Physics: Condensed Matter, 34:12 (2021) | DOI

[6] Hamilton R. W., “On quaternions; or on a new system of imaginaries in Algebra”, The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science, 25(169) (1844), 489–495 | DOI

[7] Denis J. E., Sohail M., “Singularity free algorithm for molecular dynamics simulation of rigid poly atomics”, Molecular Physics, 34:2 (1977), 327–331 | DOI

[8] Pawley G. S., “Molecular dynamics simulation of the plastic phase; a model for SF6”, Molecular Physics, 43:6 (1981), 1321–1330 | DOI

[9] Karney Ch., “Quaternions in molecular modeling”, Journal of Molecular Graphics Modelling, 25 (2007), 595–604 | DOI

[10] Miller T. F. III, Eleftheriou M., Pattnaik P., Ndirango A., Newns D., “Symplectic quaternion scheme for biophysical molecular dynamics”, The Journal of Chemical Physics, 116:20 (2002), 8649–8659 | DOI

[11] Chen P-c., Hologne M., Walker O., “Computing the Rotational Diffusion of Biomolecules via Molecular Dynamics Simulation and Quaternion Orientations”, The Journal of Physical Chemistry B, 121:8 (2017), 1812–1823 | DOI