Title

Mechanics of infinitesimal gyroscopes on helicoid-catenoid deformation family of minimal surfaces

Journal title

Bulletin of the Polish Academy of Sciences Technical Sciences

Yearbook

2021

Volume

69

Issue

2

Authors

Kovalchuk, Vasyl ; Gołubowska, Barbara ; Mladenov, Ivaïlo M.

Affiliation

Kovalchuk, Vasyl : Institute of Fundamental Technological Research, Polish Academy of Sciences, Pawińskiego 5B, 02-106 Warsaw, Poland ; Gołubowska, Barbara : Institute of Fundamental Technological Research, Polish Academy of Sciences, Pawińskiego 5B, 02-106 Warsaw, Poland ; Mladenov, Ivaïlo M. : Institute of Biophysics and Biomedical Engineering, Bulgarian Academy of Sciences, Acad. G. Bonchev Bl. 21, 1113 Sofia, Bulgaria

Keywords

action-angle analysis ; mechanics of infinitesimal gyroscopes ; geodesic and geodetic equations of motion ; helicoid-catenoid deformation family of minimal surfaces ; elliptic integrals and elliptic functions

Divisions of PAS

Nauki Techniczne

Coverage

e136727

Bibliography

1.  I.M. Mladenov and M.Ts. Hadzhilazova, “Geometry of the anisotropic minimal surfaces”, An. St. Univ. Ovidius Constanta 20, 79–88 (2012).
2.  J. Zmrzlikar, Minimal Surfaces in Biological Systems, Faculty of Mathematics and Physics, University of Ljubljana, 2011.
3.  S.N. Krivoshapko and V.N. Ivanov, Encyclopedia of Analytical Surfaces, Springer, New York-London, 2015.
4.  A. Gray, E. Abbena, and S. Salamon, Modern Differential Geometry of Curves and Surfaces with Mathematica, Chapman and Hall/CRC, New York, 2006.
5.  S. Amari and A. Cichocki, “Information geometry of divergence functions”, Bull. Pol. Acad. Sci. Tech. Sci. 58, 183–195 (2010).
6.  I.S. Gradstein and I.M. Ryzhik, Tables of Integrals, Series, and Products (7th Edition), eds. A. Jeffrey and D. Zwillinger, Academic Press, Oxford, 2007.
7.  V. Kovalchuk, B. Gołubowska, and I.M. Mladenov, “Mechanics of infinitesimal test bodies on Delaunay surfaces: spheres and cylinders as limits of unduloids and their action-angle analysis”, J. Geom. Symmetry Phys. 53, 55–84, (2019).
8.  V. Kovalchuk and I.M. Mladenov, “Mechanics of infinitesimal gyroscopes on Mylar balloons and their action-angle analysis”, Math. Meth. Appl. Sci. 43, 3040–3051 (2020).
9.  J.J. Slawianowski and B. Golubowska, “Bertrand systems on spaces of constant sectional curvature. The action-angle analysis. Classical, quasi-classical and quantum problems”, Geom. Integrability Quantization 16, 110–138 (2015).
10.  G. De Matteis, L. Martina, C. Naya, and V. Turco, “Helicoids in chiral liquid crystals under external fields”, Phys. Rev. E 100, 05273- (1–12) (2019).
11.  G. De Matteis, L. Martina, and V. Turco, “Waveguiding by helicoids in confined chiral nematics”, J. Instrum. 15, C05028-(1–11) (2020).
12.  M. Toda, F. Zhang, and B. Athukorallage, “Elastic surface model for beta-barrels: geometric, computational, and statistical analysis”, Proteins 86, 35–42 (2018).
13.  J.J. Sławianowski, V. Kovalchuk, B. Gołubowska, A. Martens, and E.E. Rożko, “Dynamical systems with internal degrees of freedom in non-Euclidean spaces”, IFTR Reports, IPPT PAN, 8/2006.

Date

08.03.2021

Type

Article

Identifier

DOI: 10.24425/bpasts.2021.136727

Source

Bulletin of the Polish Academy of Sciences: Technical Sciences; 2021; 69; 2; e136727