164 citations · 1.6k across the 59 of their papers we have counts for
60 papers
Higher order first integrals of autonomous non-Riemannian dynamical systems
Antonios Mitsopoulos, Michael Tsamparlis, Aniekan Magnus Ukpong
We consider autonomous holonomic dynamical systems defined by equations of the form , where are the…
Cubic first integrals of autonomous dynamical systems in by an algorithmic approach
Antonios Mitsopoulos, Michael Tsamparlis
In a recent paper (A. Mitsopoulos and M. Tsamparlis, J. Geom. Phys. 170, 104383, 2021), a general theorem is given which provides an algorithmic method for the computation of first…
Higher order first integrals of autonomous dynamical systems in terms of geometric symmetries
Antonios Mitsopoulos, Michael Tsamparlis
In general, a system of differential equations is integrable if there exist `sufficiently many' first integrals (FIs) so that its solution can be found by means of quadratures. The…
Integrable and superintegrable 3d Newtonian potentials using quadratic first integrals: A review
Antonios Mitsopoulos, Michael Tsamparlis
The determination of the first integrals (FIs) of a dynamical system and the subsequent assessment of their integrability or superintegrability in a systematic way is still an open…
Quadratic first integrals of constrained autonomous conservative dynamical systems with fixed energy
Antonios Mitsopoulos, Michael Tsamparlis
We consider autonomous conservative dynamical systems which are constrained with the condition that the total energy of the system has a specified value. We prove a theorem which p…
Integrable time-dependent central potentials
Antonios Mitsopoulos, Michael Tsamparlis
The integrable time-dependent central potentials that admit linear and quadratic first integrals other than those constructed from the angular momentum are determined. It is shown…