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

Kód výsledku v 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>

Výsledek na webu

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DOI - Digital Object Identifier

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Jazyk výsledku

angličtina

Název v původním jazyce

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

Popis výsledku v původním jazyce

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

Název v anglickém jazyce

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

Popis výsledku anglicky

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

Druh

J_x - Nezařazeno - Článek v odborném periodiku (Jimp, Jsc a Jost)

CEP obor

BA - Obecná matematika

OECD FORD obor

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Projekt

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Návaznosti

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

Rok uplatnění

2009

Kód důvěrnosti údajů

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Název periodika

Journal of Interdisciplinary Mathematics

ISSN

0972-0502

e-ISSN

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Svazek periodika

2009

Číslo periodika v rámci svazku

12

Stát vydavatele periodika

US - Spojené státy americké

Počet stran výsledku

12

Strana od-do

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Kód UT WoS článku

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EID výsledku v databázi Scopus

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