15 citations · 50 across the 6 of their papers we have counts for
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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…
Higher order first integrals of autonomous dynamical systems
Antonios Mitsopoulos, Michael Tsamparlis
A theorem is derived which determines higher order first integrals of autonomous holonomic dynamical systems in a general space, provided the collineations and the Killing tensors…
The generalized Ermakov conservative system: A discussion
Antonios Mitsopoulos, Michael Tsamparlis
Using older and recent results on the integrability of two-dimensional (2d) dynamical systems, we prove that the results obtained in a recent publication concerning the 2d generali…
Quadratic first integrals of time-dependent dynamical systems of the form
Antonios Mitsopoulos, Michael Tsamparlis
We consider the time-dependent dynamical system where is a non-zero arbitrary function and the connection coef…
First integrals of holonomic systems without Noether symmetries
Michael Tsamparlis, Antonios Mitsopoulos
A theorem is proved which determines the first integrals of the form of autonomous holonomic systems using only t…
Integrable and Superintegrable Potentials of 2d Autonomous Conservative Dynamical Systems
Antonios Mitsopoulos, Michael Tsamparlis, Andronikos Paliathanasis
We consider the generic quadratic first integral (QFI) of the form and require the condition . The latte…