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Acta Mechanica
Published in: Acta Mechanica 9/2021

22-06-2021 | Original Paper

Generalized Emden–Fowler equations related to constant curvature surfaces and noncentral curl forces

Author: Partha Guha

Published in: Acta Mechanica | Issue 9/2021

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Abstract

A noncentral force is a prototypical example of nonconservative position dependent force, known as curl force; this terminology was first proposed by Berry and Shukla in [1]. In this paper, we extend the construction of a noncentral force on the Euclidean plane to constant curvature spaces. It is known that the angular momentum is not conserved in a noncentral setting; we take angular momentum and integral torque to be two independent coordinates and study two different reductions of noncentral forces using these two new variables. These lead to the curvature-dependent generalized Emden–Fowler and generalized Lane–Emden equations. These reduce to the standard form of the Emden–Fowler and Lane–Emden equations when the curvature vanishes. We compute all the generalized Emden–Fowler equations based on polynomial noncentral forces. Finally, we also give a brief outline of our construction for nonpolynomial forces.
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Literature
1.
Berry, M.V., Shukla, P.: Classical dynamics with curl forces, and motion driven by time-dependent flux. J. Phys. A 45, 305201 (2012)MathSciNetCrossRef
2.
Berry, M.V., Shukla, P.: Hamiltonian curl forces. Proc. R. Soc. A 471:20150002 (13pp), (2015)
3.
4.
Chaumet, P.C., Nieto-Vesperinas, M.: Time-averaged total force on a dipolar sphere in an electromagnetic field. Opt. Lett. 25, 1065–1067 (2013)CrossRef
5.
Albaladejo, S., Marqués, M.I., Laroche, M., Sáenz, J.J.: Scattering forces from the curl of the spin angular momentum. Phys. Rev. Lett. 102, 113602 (2009)CrossRef
6.
Shimizu, Y., Sasada, H.: Mechanical force in laser cooling and trapping. Am. J. Phys. 66, 960–967 (1998)CrossRef
7.
Gutzwiller, M.C.: The anistropic kepler problem in two dimensions. J. Math. Phys. 14, 139–152 (1973)CrossRef
8.
9.
Ghose-Choudhury, A., Guha, P., Paliathanasis, A., Leach, P.G.L.: Noetherian symmetries of noncentral forces with drag term. Int. J. Geom. Methods Mod. Phys. 14, 1750018 (2017)MathSciNetCrossRef
10.
Guha, P.: Generalized Emden-Fowler equations in noncentral curl forces and first integrals. Acta Mech. 231, 815–825 (2020)MathSciNetCrossRef
11.
Guha, P.: Saddle in linear curl forces, cofactor systems and holomorphic structure. Eur. Phys. J. Plus 133, 536 (2018)CrossRef
12.
Guha, P.: Curl forces and their role in optics and ion trapping. Eur. Phys. J. D 74, 99 (2020)CrossRef
13.
Chandrasekar, S.: An Introduction to the Study of Stellar Structure. Dover, New York (1957)
14.
Richardson, O.U.: The Emission of Electricity from Hot Bodies. Longman. Green and Co., New York (1921)
15.
Davis, H.T.: Introduction to Nonlinear Differential and Integral Equations. Dover, New York (1962)
16.
17.
Mancas, S.C., Rosu, H.C.: Existence of periodic orbits in nonlinear oscillators of Emden-Fowler form. Phys. Letts A 380, 422–428 (2016)MathSciNetCrossRef
18.
Mancas, S.C., Rosu, H.C.: Two integrable classes of Emden-Fowler equations with applications in astrophysics and cosmology. Zeitschrift für Naturforschung A 73(9), 805–814 (2018)CrossRef
19.
20.
Lane, J.H.: On the theoretical temperature of the sun under the hypothesis of a gaseous mass maintaining its volume by its internal heat and depending on the laws of gases known to terrestial experiment. Am. J. Sci. Arts 4, 57–74 (1870)CrossRef
21.
Emden, R.: Gaskugeln, Anwendungen der mechanischen Warmen-theorie auf Kosmologie und meteorologische Probleme. Teubner, Leipzig (1907)
22.
Fowler, R.H.: Further studies of Emden’s and similar differential equations. Q. J. Math. 2(1), 259–288 (1931)CrossRef
23.
Böhmer, C.G., Harko, T.: Nonlinear stability analysis of the Emden-Fowler equation. J. Nonlinear Math. Phys. 17(4), 503–516 (2010)MathSciNetCrossRef
24.
Djukic, D.S.: A procedure for finding first integrals of mechanical systems with gauge-variant Lagrangians. Int. J. Non-Linear Mech. 8, 479–488 (1973)MathSciNetCrossRef
25.
Crespo Da Silva, M.R.M.: A transformation approach for finding first integrals of dynamical systems. Int. J. Non-Linear Mech. 9, 241–250 (1974)MathSciNetCrossRef
26.
27.
Guha, P., Choudhury, G.: Generalized Ermakov-Pinney and Emden-Fowler equations. Nonlinear Dyn. Syst. Theory. 14, 355–370 (2014)MathSciNetMATH
28.
Rosu, H., Mancas, S.: Generalized Thomas-Fermi equations as the Lampariello class of Emden-Fowler equations. Physica A: Stat. Mech. Appl. 471, 212–218 (2017)MathSciNetCrossRef
29.
Lobachevskij, N.I.: 1949, In Collected Works (GITTL. Moscow 2, 159 (1949)
30.
Serret 1860, Théorie nouvelle géometrique et mécanique des lignes a double Pcourbure, (Librave de Mallet-Bachelier: Paris, 1860)
31.
Killing, W.: Die mechanik in den nicht-Euklidischen raumformen. J. Reine Angew. Math. 98, 1–48 (1885)MathSciNetMATH
32.
Liebmann, H.: Uber die Zentralbewegung in der Nichteuklidische Geometrie. Leipzig Ber. 55, 146–153 (1903)
33.
Carinena, J.F., Ranada, M.F., Santander, M.: Central potentials on spaces of constant curvature: the Kepler problem on the two-dimensional sphere S2 and the hyperbolic plane H2. J. Math. Phys. 46, 052702 (2005)MathSciNetCrossRef
34.
Ballesteros, A., Herranz, F.J.: Maximal superintegrability of the generalized Kepler-Coulomb system on N-dimensional curved spaces. J. Phys. A: Math. Theor. 42, 245203 (2009)MathSciNetCrossRef
35.
Ballesteros, A., Blasco, A., Herranz, F.J., Musso, F.: A new integrable anisotropic oscillator on the two- dimensional sphere and the hyperbolic plane. J. Phys. A Math. Theor 47, 345204 (2014). (21pp)MathSciNetCrossRef
36.
Ballesteros, A., Encisco, A., Herranz, F.J., Ragnisco, O.: Superintegrability on N-dimensional curved spaces: central potentials, centrifugal terms and monopoles. Ann. Phys. 324, 1219–1233 (2009)MathSciNetCrossRef
37.
38.
Diacu, F., Perez-Chavela, E., Santoprete, M.: (2008) The n-body problem in spaces of constant curvature, arXiv preprint arXiv:​0807.​1747
Metadata
Title
Generalized Emden–Fowler equations related to constant curvature surfaces and noncentral curl forces
Author
Partha Guha
Publication date
22-06-2021
Publisher
Springer Vienna
Published in
Acta Mechanica / Issue 9/2021
Print ISSN: 0001-5970
Electronic ISSN: 1619-6937
DOI
https://doi.org/10.1007/s00707-021-02998-3

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