2022 # Quadratic First Integrals of Constrained Autonomous Conservative Dynamical Systems with Fixed Energy

**Abstract:** 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 provides the quadratic first integrals (QFIs), time-dependent and autonomous, of these systems in terms of the symmetries (conformal Killing vectors and conformal Killing tensors) of the kinetic metric. It is proved that there are three types of QFIs and for each type we give explicit formulae for their computation. It is also shown t…

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2023

2023

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“…The associated kinetic metric is γ ab = F (x, y) 0 1 1 0 . The constrained geodesics of this metric has been discussed for various cases of the function F (x, y) in [11] and, more recently, in [12]…”

confidence: 99%

“…The associated kinetic metric is γ ab = F (x, y) 0 1 1 0 . The constrained geodesics of this metric has been discussed for various cases of the function F (x, y) in [11] and, more recently, in [12]…”

confidence: 99%