Force Evolutionary Billiards and Billiard Equivalence of the Euler and Lagrange Cases
V. V. Vedyushkina, А. Т. Фоменко
Abstract
Abstract A class of force evolutionary billiards is discovered that realizes important integrable Hamiltonian systems on all regular isoenergy 3-surfaces simultaneously, i.e., on the phase 4-space. It is proved that the well-known Euler and Lagrange integrable systems are billiard equivalent, although the degrees of their integrals are different (two and one).
Topics & Concepts
Dynamical billiardsIntegrable systemMathematicsPhase spaceHamiltonian systemKolmogorov–Arnold–Moser theoremEuler's formulaEquivalence (formal languages)Class (philosophy)LagrangianClassical mechanicsPure mathematicsMathematical analysisPhysicsGeometryQuantum mechanicsComputer scienceArtificial intelligenceQuantum chaos and dynamical systemsMathematical Dynamics and FractalsAdvanced Differential Equations and Dynamical Systems