Non-integrability of a rotating elliptic billiard (Q2714640)

The author considers the motion of a point inside a rotating ellipse. It is assumed that the collisions with the boundary are absolutely elastic. The equation of the boundary of domain \(\partial D\) in the coordinates \(x\) and \(y\) is of the form \(\,x^2/a^2 + y^2/b^2 = 1\), \(\,0<b^2\leq a^2\). For this problem the Lagrange function in the generalized coordinates \(x\) and \(y\) is \(L = \tfrac12\,(\dot x^2 + \dot y^2) + \varepsilon(x\dot y- \dot xy) + o(\varepsilon).\) It is established that this dynamical system does not admit an analytical integral independent of the energy integral.