The applicability of the third integral of motion: Some numerical experiments

Key Points

• The research aims to explore the existence of a third isolating integral of motion in axisymmetric potentials.
• Conducted numerical experiments to examine the third integral of motion in axisymmetric potential.
• Assessed a range of initial conditions to determine the presence of the third integral.
• The third integral exists only within a limited range of initial conditions.
• Findings indicate that not all initial conditions allow for the existence of the third integral.