{"id":{"repo_id":"brazil-uerj","oai_identifier":"oai:pantheon.ufrj.br:11422/3737"},"canonical_url":"https://search.dev.ndltd.org/etd/brazil-uerj/oai:pantheon.ufrj.br:11422/3737","repository":{"repo_id":"brazil-uerj","name":"Brazil UERJ","base_url":"https://pantheon.ufrj.br/oai/request"},"display":{"title":"Domínios de estabilidade assintótica: sua determinação utilizando o segundo Método de Liapunov","abstract":"Presents some methods to determine the domains of asyntotical stability of the trivial solution of first-order, non-linear, differential equations when Liapnov's second (direct) method is used. The first three chapters are introductory and present an historical review, the use of quadratic forms as Liapunov's functions, and a physical interpretation of the mathematical treatment. Chapter 4 presents an application of Linear System Theory to autonomous systems, and the determination of the ellipticals and sphericals domains of stability. A logical procedure of the criterium is also presented. The following chapters introduce the Schultz Gibson's and Zubov's methods. The first uses a line integral of the gradient of Liapunov's function. The second uses a partial differential equation that, as long as it has a closed-form solution, allows the determination os the exact domain of asyntotic stability. All the concepts considered essentials are introduced · in order to obtain a self- contained work as such as possible.","abstract_html":"Presents some methods to determine the domains of asyntotical stability of the trivial solution of first-order, non-linear, differential equations when Liapnov's second (direct) method is used. The first three chapters are introductory and present an historical review, the use of quadratic forms as Liapunov's functions, and a physical interpretation of the mathematical treatment. Chapter 4 presents an application of Linear System Theory to autonomous systems, and the determination of the ellipticals and sphericals domains of stability. A logical procedure of the criterium is also presented. The following chapters introduce the Schultz Gibson's and Zubov's methods. The first uses a line integral of the gradient of Liapunov's function. The second uses a partial differential equation that, as long as it has a closed-form solution, allows the determination os the exact domain of asyntotic stability. All the concepts considered essentials are introduced · in order to obtain a self- contained work as such as possible.","abstract_has_math":false,"creators":["Fonseca, Luiz Gonzaga de Souza"],"institution":"Universidade Federal do Rio de Janeiro","degree_name":null,"degree_level":null,"degree_discipline":null,"degree_department":null,"school":null,"contributors":[],"advisors":["Ribeiro, Demétrio Alonso"],"committee_chairs":[],"committee_members":[],"year":1971,"date_issued":"1971-01","date_published":"1971-01","updated_at":"2026-07-24T01:16:10Z","subjects":["Engenharia elétrica","Sistemas não-lineares","Equações diferenciais ordinárias","Liapunov, Funções de"],"languages":["por"],"rights":["Acesso Aberto"],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"http://hdl.handle.net/11422/3737","outbound_label":"Handle","outbound_source":"dc:identifier.uri"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor.advisor","label":"Advisor","values":["Ribeiro, Demétrio Alonso"]},{"key":"dc:creator","label":"Author","values":["Fonseca, Luiz Gonzaga de Souza"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date.accessioned","label":"Dc Date Accessioned","values":["2018-03-15T14:52:18Z"]},{"key":"dc:date.available","label":"Dc Date Available","values":["2026-05-16T03:05:20Z"]},{"key":"dc:date.issued","label":"Date","values":["1971-01"]},{"key":"dc:publisher","label":"Institution","values":["Universidade Federal do Rio de Janeiro"]},{"key":"dc:publisher.department","label":"Dc Publisher Department","values":["Instituto Alberto Luiz Coimbra de Pós-Graduação e Pesquisa de Engenharia"]},{"key":"dc:type","label":"Dc Type","values":["Dissertação"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["Engenharia elétrica","Sistemas não-lineares","Equações diferenciais ordinárias","Liapunov, Funções de"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:language","label":"Dc Language","values":["por"]},{"key":"dc:rights","label":"Dc Rights","values":["Acesso Aberto"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier.uri","label":"Identifier URI","values":["http://hdl.handle.net/11422/3737"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description.abstract","label":"Abstract","values":["Presents some methods to determine the domains of asyntotical stability of the trivial solution of first-order, non-linear, differential equations when Liapnov's second (direct) method is used. The first three chapters are introductory and present an historical review, the use of quadratic forms as Liapunov's functions, and a physical interpretation of the mathematical treatment. Chapter 4 presents an application of Linear System Theory to autonomous systems, and the determination of the ellipticals and sphericals domains of stability. A logical procedure of the criterium is also presented. The following chapters introduce the Schultz Gibson's and Zubov's methods. The first uses a line integral of the gradient of Liapunov's function. The second uses a partial differential equation that, as long as it has a closed-form solution, allows the determination os the exact domain of asyntotic stability. All the concepts considered essentials are introduced · in order to obtain a self- contained work as such as possible."]},{"key":"dc:title","label":"Title","values":["Domínios de estabilidade assintótica: sua determinação utilizando o segundo Método de Liapunov"]}]}],"canonical_facts":{"dc:contributor.advisor":["Ribeiro, Demétrio Alonso"],"dc:creator":["Fonseca, Luiz Gonzaga de Souza"],"dc:date.accessioned":["2018-03-15T14:52:18Z"],"dc:date.available":["2026-05-16T03:05:20Z"],"dc:date.issued":["1971-01"],"dc:description.abstract":["Presents some methods to determine the domains of asyntotical stability of the trivial solution of first-order, non-linear, differential equations when Liapnov's second (direct) method is used. The first three chapters are introductory and present an historical review, the use of quadratic forms as Liapunov's functions, and a physical interpretation of the mathematical treatment. Chapter 4 presents an application of Linear System Theory to autonomous systems, and the determination of the ellipticals and sphericals domains of stability. A logical procedure of the criterium is also presented. The following chapters introduce the Schultz Gibson's and Zubov's methods. The first uses a line integral of the gradient of Liapunov's function. The second uses a partial differential equation that, as long as it has a closed-form solution, allows the determination os the exact domain of asyntotic stability. All the concepts considered essentials are introduced · in order to obtain a self- contained work as such as possible."],"dc:identifier.uri":["http://hdl.handle.net/11422/3737"],"dc:language":["por"],"dc:publisher":["Universidade Federal do Rio de Janeiro"],"dc:publisher.department":["Instituto Alberto Luiz Coimbra de Pós-Graduação e Pesquisa de Engenharia"],"dc:rights":["Acesso Aberto"],"dc:subject":["Engenharia elétrica","Sistemas não-lineares","Equações diferenciais ordinárias","Liapunov, Funções de"],"dc:title":["Domínios de estabilidade assintótica: sua determinação utilizando o segundo Método de Liapunov"],"dc:type":["Dissertação"]},"updated_at":"2026-07-24T01:16:10Z"}