Continuation of Periodic Solutions of Dissipative and Conservative Systems - Application to Elastic Pendulum.

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F60461373%3A22340%2F09%3A00021944" target="_blank" >RIV/60461373:22340/09:00021944 - 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

Continuation of Periodic Solutions of Dissipative and Conservative Systems - Application to Elastic Pendulum.

Popis výsledku v původním jazyce

Continuation is an efficient algorithm for finding solutions of systems of nonlinear algebraic equations where the solutions form a one-dimensional continuum. Such systems arise naturally when investigating equilibrium points and periodic solutions of ordinary differential equations with one parameter. Continuation of isolated periodic solutions of dissipative systems is a well- established technique. Less attention has been devoted to continuation of periodic solutions of conservative systems, where periodic solutions typically form a one-parameter family. To specify a single periodic solution, additional condition must be considered. However, this gives an over- determined system, which has no solution when working with approximate numerical values.We propose a simple algorithm which solves this difficulty by using singular value decomposition of the Jacobian matrix. This algorithm is applied to the conservative model of elastic pendulum. A branch of periodic solutions with constant

Název v anglickém jazyce

Continuation of Periodic Solutions of Dissipative and Conservative Systems - Application to Elastic Pendulum.

Popis výsledku anglicky

Continuation is an efficient algorithm for finding solutions of systems of nonlinear algebraic equations where the solutions form a one-dimensional continuum. Such systems arise naturally when investigating equilibrium points and periodic solutions of ordinary differential equations with one parameter. Continuation of isolated periodic solutions of dissipative systems is a well- established technique. Less attention has been devoted to continuation of periodic solutions of conservative systems, where periodic solutions typically form a one-parameter family. To specify a single periodic solution, additional condition must be considered. However, this gives an over- determined system, which has no solution when working with approximate numerical values.We propose a simple algorithm which solves this difficulty by using singular value decomposition of the Jacobian matrix. This algorithm is applied to the conservative model of elastic pendulum. A branch of periodic solutions with constant

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)

Rok uplatnění

2009

Kód důvěrnosti údajů

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

Název periodika

Mathematical Problems in Engineering

ISSN

1024-123X

e-ISSN

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Svazek periodika

2009

Číslo periodika v rámci svazku

1

Stát vydavatele periodika

US - Spojené státy americké

Počet stran výsledku

15

Strana od-do

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Kód UT WoS článku

000267562200001

EID výsledku v databázi Scopus

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