On the periodic motion of one-dimensional oscillator between two elastic walls
J. Babováková, Petr Nečesal · Journal of Interdisciplinary Mathematics · 2009
We investigate the periodic solutions of a one-dimensional nonlinear pendulum where y + := max{y, 0} and y − := max{ − y, 0} . The pendulum is located between two one-sided springs with stiffnesses k 1 and k 2 in distances r 1 and r 2 . For the first approximation, we investigate the simplified model without damping ( δ = 0 ) and with zero righthand side In the symmetric case of r 1 = r 2 and k 1 = k 2 , we give the full and precise description of the solution set of the problem ( * ) with respect to its parameters. We prove the existence of multiple solutions of ( * ) and moreover, we provide the qualitative properties of the corresponding solution diagram. Finally, we reconstruct the solution diagram for the problem ( * ) also in the case of general non-symmetric settings of its parameters k , k 1 , k 2 , r 1 , r 2 and T .