Fetching the paper…
Reading the bibliography…
Certain dissipative systems, such as Caldirola and Kannai's damped simple harmonic oscillator, may be modelled by time-dependent Lagrangian and hence time dependent Hamiltonian systems with $n$ degrees of freedom.
J. Mestschersky, “Ein Spezialfall der Gyldén’schen Problem (A.N. 2593),” Astronomische Nachrichten 132
1902
Earlier work this paper cites.
H. W. Brinkmann, “Einstein spaces which are mapped conformally on each other,” Math. Ann. 94
1925
Earlier work this paper cites.
L. P. Eisenhart, “Dynamical trajectories and geodesics”, Annals. Math. 30
1928
Earlier work this paper cites.
A. Liénard, “Etude des oscillations entretenues,” Revue générale de l’électricité, 23
1928
Earlier work this paper cites.
B. van der Pol, “On relaxation-oscillations,” The London, Edinburgh and Dublin Philosophical Magazine and Journal of Science 2
1928
Earlier work this paper cites.
H. Bateman, “On dissipative systems and related variational principles,” Phys. Rev. 38
1931
Earlier work this paper cites.
G. C. McVittie, The mass-particle in an expanding universe,” Mon. Not. Roy. Astron. Soc. 93
1933
Earlier work this paper cites.
P. A. M. Dirac, “The cosmological constants,” Nature, 139
1938
Earlier work this paper cites.
P. Caldirola, “Forze non-conservative nella meccanica quantistica,” Nuovo Cimento, 18
1941
Earlier work this paper cites.
E. Kanai, “On the Quantization of the Dissipative Systems” Prog. Theor. Phys., 3
1948
Earlier work this paper cites.
B. Hoffmann, “Kron’s Non-Riemannian Electrodynamics,” Rev. Mod. Phys. 21
1949
Earlier work this paper cites.
G C McVittie, General Relativity and Cosmology
1964
Earlier work this paper cites.
N. A. Dmitriev and Ya. B. Zel’dovich, “The energy of accidental motions in the expanding universe,” Sov. Phys. JETP 18
1964
Earlier work this paper cites.
V.I. Arnold, “Sur la géométrie différentielle des groupes de Lie de dimension infinie et ses applications à l’hydrodynamique des fluides parfaits,” Ann. Inst. Fourier 16
1966
Earlier work this paper cites.
R. Jackiw, “Introducing scale symmetry,” Phys. Today 25
1972
Earlier work this paper cites.
U. Niederer, “The maximal kinematical invariance group of the free Schrödinger equation.” Helv. Phys. Acta 45
1972
Earlier work this paper cites.
C. R. Hagen, C. R. Hagen, “Scale and conformal transformations in galilean-covariant field theory,” Phys. Rev. D 5
1972
Earlier work this paper cites.
U. Niederer, “The maximal kinematical invariance group of the harmonic oscillator,” Helv. Phys. Acta 46
1973
Earlier work this paper cites.
J.P. Vinti, “Classical solution of the two-body problem if the gravitational constant diminishes inversely with the age of the universe,” Not. Roy. Astron. Soc. 169
1974
Earlier work this paper cites.
G. W. Gibbons, “Quantized Fields Propagating in Plane Wave Space-Times,” Commun. Math. Phys. 45
1975
Earlier work this paper cites.
J. Gomis and J. M. Pons, “Poincare Transformations and Galilei Transformations,” Phys. Lett. A 66
1978
Cited alongside, same era.
H. Goldstein, Classical Mechanics
1980
Cited alongside, same era.
P J E Peebles, “The Large-scale structure of the universe,” Princeton University Press, Princeton, NJ (1980)
1980
Cited alongside, same era.
H. Dekker, “Classical and quantum mechanics of the damped harmonic oscillator,” Phys. Rept. 80
1981
Cited alongside, same era.
D. Lynden-Bell, “On the N N -body problem in Dirac’s cosmology,” Observatory 102
1982
Cited alongside, same era.
V. I. Arnold, Supplementary Chapters to the Theory of Ordinary Differential Equations
1983
Cited alongside, same era.
C. I. Um, K. H. Yeon and T. F. George, “The Quantum damped harmonic oscillator,” Phys. Rept. 362
2002
Later among the works it cites.
G.W. Gibbons and C.E.Patricot, “Newton-Hooke spacetimes, Hpp-waves and the cosmological constant”, Class. Quant. Grav
2003
Later among the works it cites.
A. V. Aminova and N. A-M Aminov, “Projective geometry of systems of second-order differential equations,” Sbornik Mathematics 197
2006
Later among the works it cites.
2008
Later among the works it cites.
C. Duval and P. A. Horvathy, “Non-relativistic conformal symmetries and Newton-Cartan structures,” J. Phys. A42
2009
Later among the works it cites.
alphaXiv searches the wider corpus for related work and actual follow-ups.
alphaXiv is searching for related work…
J. Cerverò and J. Villarroel, “ S L ( 3 , ℝ ) SL(3,{\mathbb{R}}) realisations and the damped harmonic oscillator”, J. Phys. A 17
1984
Cited alongside, same era.
C. Duval, G. Burdet, H. P. Künzle and M. Perrin, “Bargmann Structures and Newton-Cartan Theory,” Phys. Rev. D 31
1985
Cited alongside, same era.
G. Burdet, C. Duval and M. Perrin, “Time-Dependent Quantum Systems and Chronoprojective Geometry”, Lett. Math. Phys. 10
1985
Cited alongside, same era.
A. P. Balachandran, H. Gomm and R. D. Sorkin, “Quantum Symmetries From Quantum Phases: Fermions From Bosons, a Z Z (2) Anomaly and Galilean Invariance,” Nucl. Phys. B 281
1987
Cited alongside, same era.
T. Damour, G. W. Gibbons and J. H. Taylor, “Limits on the Variability of G Using Binary-Pulsar Data,” Phys. Rev. Lett. 61
1988
Cited alongside, same era.
C. Duval, G. W. Gibbons and P. Horvathy, “Celestial mechanics, conformal structures and gravitational waves,” Phys. Rev. D 43
1991
Cited alongside, same era.
2011
Later among the works it cites.
2011
Later among the works it cites.
2011
Later among the works it cites.
P. M. Zhang and P. A. Horvathy, “Kohn’s theorem and Galilean symmetry,” Phys. Lett. B 702
2011
Later among the works it cites.
J. Guerrero, V. Aldaya, F. F. López-Ruiz and F. Cossío, “Unfolding the quantum Arnold transformation,” Int. J. Geom. Meth. Mod. Phys. 09
2012
Later among the works it cites.
V. Aldaya, F. Cossío, J. Guerrero and F. F. López-Ruiz, Private communication (2013)
2013
Later among the works it cites.
M. Cariglia, “Hidden Symmetries of Dynamics in Classical and Quantum Physics,” Rev. Mod. Phys. 86
2014
Later among the works it cites.
G. F. R. Ellis and G. W. Gibbons, “Discrete Newtonian Cosmology,” Class. Quant. Grav. 31
2014
Later among the works it cites.
2015
Later among the works it cites.
E. Minguzzi, “Rayleigh’s dissipation function at work,” Eur. J. Phys. 36
2015
Later among the works it cites.
2015
Later among the works it cites.
2015
Later among the works it cites.
H. Kyono and K. Yoshida, “Yang-Baxter invariance of the Nappi-Witten model,” Nucl. Phys. B 905
2016
Closest in time.
S. Benenti, “Mathematical models in isotropic cosmology”, Working Paper April 2016. DOI: 10.13140/RG.2.1.191.8800
2016
Closest in time.