On the periodic motion of one-dimensional oscillator between two elastic walls

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F49777513%3A23520%2F09%3A00501684" target="_blank" >RIV/49777513:23520/09:00501684 - isvavai.cz</a>
Result on the web
—
DOI - Digital Object Identifier
—

Result language
angličtina
Original language name
On the periodic motion of one-dimensional oscillator between two elastic walls
Original language description
We investigate the periodic solutions of a one-dimensional nonlinear pendulum $y'' + delta y' + k sin y + k_{1}(y - r_{1})^{+} - k_{2}(y + r_{2})^{-} = f$, 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 ($delta = 0$) and with zero right-hand side $y'' + k y + k_{1}(y - r_{1})^{+} - k_{2}(y +r_{2})^{-} = 0$ together with periodic condition $y(t) = y(t+T)$. 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 simplified problem with respect to its parameters. We prove the existence of multiple solutions and moreover, we provide the qualitative properties of the corresponding solution diagram. Finally, we reconstruct the solution diagram for the simplified problem also in the case of genera
Czech name
—
Czech description
—

Type
J<sub>x</sub> - Unclassified - Peer-reviewed scientific article (Jimp, Jsc and Jost)
CEP classification
BA - General mathematics
OECD FORD branch
—

Project
—
Continuities
Z - Vyzkumny zamer (s odkazem do CEZ)<br>S - Specificky vyzkum na vysokych skolach

Publication year
2009
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Similar results(10)