Bounce trajectories with one bounce point (Q1191330)

The author considers a mechanical system with a potential force in a connected bounded domain \(\Omega\) in \(\mathbb{R}^ n\) with \(C^ 2\)-smooth boundary. He obtains the condition under which for given points \(A,B\in \Omega\) and \(T>0\) there exists a trajectory \(\gamma\) of the system ``bouncing'' exactly one time from the boundary and such that \(\gamma(0)=A\) and \(\gamma(T)=B\).