Quadratic First Integrals of Time-Dependent Dynamical Systems of the Form <inline-formula><math display="inline"><semantics><mstyle mathvariant="bold"><mrow><msup><mover accent="true"><mi mathvariant="bold-italic">q</mi><mo>¨</mo></mover><mi mathvariant="bold-italic">a</mi></msup><mo>=</mo><mo>−</mo><msubsup><mo>Γ</mo><mrow><mi mathvariant="bold-italic">b</mi><mi mathvariant="bold-italic">c</mi></mrow><mi mathvariant="bold-italic">a</mi></msubsup><msup><mover accent="true"><mi mathvariant="bold-italic">q</mi><mo>˙</mo></mover><mi mathvariant="bold-italic">b</mi></msup><msup><mover accent="true"><mi mathvariant="bold-italic">q</mi><mo>˙</mo></mover><mi mathvariant="bold-italic">c</mi></msup><mo>−</mo><mi mathvariant="bold-italic">ω</mi><mrow><mo>(</mo><mi mathvariant="bold-italic">t</mi><mo>)</mo></mrow><msup><mi mathvariant="bold-italic">Q</mi><mi mathvariant="bold-italic">a</mi></msup><mrow><mo>(</mo><mi mathvariant="bold-italic">q</mi><mo>)</mo></mrow></mrow></mstyle></semantics></math></inline-formula>

We consider the time-dependent dynamical system <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msup><mover accent="true"><mi>q</mi><mo>¨</mo></mover>&l...

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Bibliographic Details

Main Authors:	Antonios Mitsopoulos, Michael Tsamparlis
Format:	Article
Language:	English
Published:	MDPI AG 2021-06-01
Series:	Mathematics
Subjects:	time-dependent dynamical systems quadratic first integrals Killing tensors kinetic metric Kepler potential oscillator
Online Access:	https://www.mdpi.com/2227-7390/9/13/1503