The developments of Analytical Mechanics which culminated on the elaboration of F = ma
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Data de Publicação: | 2019 |
Tipo de documento: | Artigo |
Idioma: | por |
Título da fonte: | Caderno Brasileiro de Ensino de Física (Online) |
Texto Completo: | https://periodicos.ufsc.br/index.php/fisica/article/view/2175-7941.2019v36n1p158 |
Resumo: | Newton's law and F = ma are different principles. About sixty years of conceptual and mathematical developments were necessary for the Second Law of Motion could be elaborated, around 1752 to 1776, by Leonhard Euler. In this research, we discuss the main factors referring to the construction of this law, which made possible for Euler, and no other, to obtain the Second Law of Motion, as we know it today. We also discuss what was being done in mechanics at early eighteenth century and how it contributed for the elaboration of the conceptual bases, thus making possible the emergence of the Second Law of Motion as a general principle of mechanics, such as the search for generalization of principles, the introduction of analytical mechanics, with new techniques and mathematical tools, the study of certain problems, the unification of concepts and the elaboration of alternative bases for mechanics, like the variational principles. These achievements contributed so that Euler could refine and extend Newton’s Law to much larger degree of problems. |
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The developments of Analytical Mechanics which culminated on the elaboration of F = maOs desenvolvimentos da Mecânica Analítica que culminaram na elaboração de F=maNewton's law and F = ma are different principles. About sixty years of conceptual and mathematical developments were necessary for the Second Law of Motion could be elaborated, around 1752 to 1776, by Leonhard Euler. In this research, we discuss the main factors referring to the construction of this law, which made possible for Euler, and no other, to obtain the Second Law of Motion, as we know it today. We also discuss what was being done in mechanics at early eighteenth century and how it contributed for the elaboration of the conceptual bases, thus making possible the emergence of the Second Law of Motion as a general principle of mechanics, such as the search for generalization of principles, the introduction of analytical mechanics, with new techniques and mathematical tools, the study of certain problems, the unification of concepts and the elaboration of alternative bases for mechanics, like the variational principles. These achievements contributed so that Euler could refine and extend Newton’s Law to much larger degree of problems.A lei de Newton e F = ma são princípios diferentes. Cerca de sessenta anos de desenvolvimentos conceituais e matemáticos foram necessários para que a Segunda Lei do Movimento fosse elaborada, em 1752-1776, pelas mãos de Leonhard Euler. Neste trabalho, são discutidos os principais desses fatores adjacentes à construção dessa lei, sem os quais não seria possível Euler, e nenhum outro, obter a Segunda Lei do Movimento, como a conhecemos hoje. Será discutido o que estava sendo feito na mecânica no início do século XVIII e que contribuiu para que bases conceituais fossem elaboradas para que então fosse possível a emergência da Segunda Lei do Movimento como um princípio geral da mecânica, como a busca pela generalização de princípios, a introdução da mecânica analítica, com novas técnicas e ferramentais matemáticos, o estudo de determinados tipos de problemas, a unificação de conceitos e a elaboração de bases alternativas para a mecânica, como os princípios variacionais. Essas realizações contribuíram para que a lei proposta por Newton fosse aperfeiçoada e ampliada por Euler para uma classe muito maior de problemas.Imprensa Universitária - UFSC2019-05-13info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionapplication/pdfhttps://periodicos.ufsc.br/index.php/fisica/article/view/2175-7941.2019v36n1p15810.5007/2175-7941.2019v36n1p158Caderno Brasileiro de Ensino de Física; v. 36 n. 1 (2019); 158-1772175-79411677-2334reponame:Caderno Brasileiro de Ensino de Física (Online)instname:Universidade Federal de Santa Catarina (UFSC)instacron:UFSCporhttps://periodicos.ufsc.br/index.php/fisica/article/view/2175-7941.2019v36n1p158/39936Copyright (c) 2019 Caderno Brasileiro de Ensino de Físicainfo:eu-repo/semantics/openAccessSitko, Camila Maria2019-07-25T15:24:27Zoai:periodicos.ufsc.br:article/60780Revistahttp://www.periodicos.ufsc.br/index.php/fisicaPUBhttps://periodicos.ufsc.br/index.php/fisica/oaicbefisica@gmail.com||fscccef@fsc.ufsc.br|| cbefisica@gmail.com2175-79411677-2334opendoar:2019-07-25T15:24:27Caderno Brasileiro de Ensino de Física (Online) - Universidade Federal de Santa Catarina (UFSC)false |
dc.title.none.fl_str_mv |
The developments of Analytical Mechanics which culminated on the elaboration of F = ma Os desenvolvimentos da Mecânica Analítica que culminaram na elaboração de F=ma |
title |
The developments of Analytical Mechanics which culminated on the elaboration of F = ma |
spellingShingle |
The developments of Analytical Mechanics which culminated on the elaboration of F = ma Sitko, Camila Maria |
title_short |
The developments of Analytical Mechanics which culminated on the elaboration of F = ma |
title_full |
The developments of Analytical Mechanics which culminated on the elaboration of F = ma |
title_fullStr |
The developments of Analytical Mechanics which culminated on the elaboration of F = ma |
title_full_unstemmed |
The developments of Analytical Mechanics which culminated on the elaboration of F = ma |
title_sort |
The developments of Analytical Mechanics which culminated on the elaboration of F = ma |
author |
Sitko, Camila Maria |
author_facet |
Sitko, Camila Maria |
author_role |
author |
dc.contributor.author.fl_str_mv |
Sitko, Camila Maria |
description |
Newton's law and F = ma are different principles. About sixty years of conceptual and mathematical developments were necessary for the Second Law of Motion could be elaborated, around 1752 to 1776, by Leonhard Euler. In this research, we discuss the main factors referring to the construction of this law, which made possible for Euler, and no other, to obtain the Second Law of Motion, as we know it today. We also discuss what was being done in mechanics at early eighteenth century and how it contributed for the elaboration of the conceptual bases, thus making possible the emergence of the Second Law of Motion as a general principle of mechanics, such as the search for generalization of principles, the introduction of analytical mechanics, with new techniques and mathematical tools, the study of certain problems, the unification of concepts and the elaboration of alternative bases for mechanics, like the variational principles. These achievements contributed so that Euler could refine and extend Newton’s Law to much larger degree of problems. |
publishDate |
2019 |
dc.date.none.fl_str_mv |
2019-05-13 |
dc.type.driver.fl_str_mv |
info:eu-repo/semantics/article info:eu-repo/semantics/publishedVersion |
format |
article |
status_str |
publishedVersion |
dc.identifier.uri.fl_str_mv |
https://periodicos.ufsc.br/index.php/fisica/article/view/2175-7941.2019v36n1p158 10.5007/2175-7941.2019v36n1p158 |
url |
https://periodicos.ufsc.br/index.php/fisica/article/view/2175-7941.2019v36n1p158 |
identifier_str_mv |
10.5007/2175-7941.2019v36n1p158 |
dc.language.iso.fl_str_mv |
por |
language |
por |
dc.relation.none.fl_str_mv |
https://periodicos.ufsc.br/index.php/fisica/article/view/2175-7941.2019v36n1p158/39936 |
dc.rights.driver.fl_str_mv |
Copyright (c) 2019 Caderno Brasileiro de Ensino de Física info:eu-repo/semantics/openAccess |
rights_invalid_str_mv |
Copyright (c) 2019 Caderno Brasileiro de Ensino de Física |
eu_rights_str_mv |
openAccess |
dc.format.none.fl_str_mv |
application/pdf |
dc.publisher.none.fl_str_mv |
Imprensa Universitária - UFSC |
publisher.none.fl_str_mv |
Imprensa Universitária - UFSC |
dc.source.none.fl_str_mv |
Caderno Brasileiro de Ensino de Física; v. 36 n. 1 (2019); 158-177 2175-7941 1677-2334 reponame:Caderno Brasileiro de Ensino de Física (Online) instname:Universidade Federal de Santa Catarina (UFSC) instacron:UFSC |
instname_str |
Universidade Federal de Santa Catarina (UFSC) |
instacron_str |
UFSC |
institution |
UFSC |
reponame_str |
Caderno Brasileiro de Ensino de Física (Online) |
collection |
Caderno Brasileiro de Ensino de Física (Online) |
repository.name.fl_str_mv |
Caderno Brasileiro de Ensino de Física (Online) - Universidade Federal de Santa Catarina (UFSC) |
repository.mail.fl_str_mv |
cbefisica@gmail.com||fscccef@fsc.ufsc.br|| cbefisica@gmail.com |
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1799940574385537024 |