coordenadas curvilíneas
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Coordenadas CurvilíneasTRANSCRIPT
![Page 1: Coordenadas Curvilíneas](https://reader034.vdocuments.pub/reader034/viewer/2022051621/55cf8fed550346703ba15889/html5/thumbnails/1.jpg)
Professor: Márcio André Araújo Cavalcante
Coordenadas Curvilíneas
Universidade Federal de Alagoas – UFAL
Centro de Tecnologia - CTEC
Programa de Pós-Graduação em Engenharia Civil - PPGEC
Introdução à Mecânica do Contínuo
Maceió - Alagoas
![Page 2: Coordenadas Curvilíneas](https://reader034.vdocuments.pub/reader034/viewer/2022051621/55cf8fed550346703ba15889/html5/thumbnails/2.jpg)
Coordenadas Polares
Coordenadas Polares (r,q):
Relação entre os vetores unitários que definem as bases:
![Page 3: Coordenadas Curvilíneas](https://reader034.vdocuments.pub/reader034/viewer/2022051621/55cf8fed550346703ba15889/html5/thumbnails/3.jpg)
Coordenadas Polares
Gradiente de um Campo Escalar f(r,q):
Gradiente de um Campo Vetorial v(r,q):
![Page 4: Coordenadas Curvilíneas](https://reader034.vdocuments.pub/reader034/viewer/2022051621/55cf8fed550346703ba15889/html5/thumbnails/4.jpg)
Coordenadas Polares
Divergente de um Campo Vetorial v(r,q):
Divergente de um Campo Tensorial T(r,q):
![Page 5: Coordenadas Curvilíneas](https://reader034.vdocuments.pub/reader034/viewer/2022051621/55cf8fed550346703ba15889/html5/thumbnails/5.jpg)
Coordenadas Polares
Laplaciano de um Campo Escalar f(r,q):
Laplaciano de um Campo Vetorial v(r,q):
![Page 6: Coordenadas Curvilíneas](https://reader034.vdocuments.pub/reader034/viewer/2022051621/55cf8fed550346703ba15889/html5/thumbnails/6.jpg)
Coordenadas Cilíndricas
Coordenadas Cilíndricas (r,q,z):
Relação entre os vetores unitários que definem as bases:
![Page 7: Coordenadas Curvilíneas](https://reader034.vdocuments.pub/reader034/viewer/2022051621/55cf8fed550346703ba15889/html5/thumbnails/7.jpg)
Gradiente de um Campo Escalar f(r,q,z):
Gradiente de um Campo Vetorial v(r,q,z):
Coordenadas Cilíndricas
![Page 8: Coordenadas Curvilíneas](https://reader034.vdocuments.pub/reader034/viewer/2022051621/55cf8fed550346703ba15889/html5/thumbnails/8.jpg)
Coordenadas Cilíndricas
Divergente de um Campo Vetorial v(r,q,z):
Divergente de um Campo Tensorial T(r,q,z):
![Page 9: Coordenadas Curvilíneas](https://reader034.vdocuments.pub/reader034/viewer/2022051621/55cf8fed550346703ba15889/html5/thumbnails/9.jpg)
Coordenadas Cilíndricas
Laplaciano de um Campo Escalar f(r,q,z):
Laplaciano de um Campo Vetorial v(r,q,z):
![Page 10: Coordenadas Curvilíneas](https://reader034.vdocuments.pub/reader034/viewer/2022051621/55cf8fed550346703ba15889/html5/thumbnails/10.jpg)
Coordenadas Esféricas
Coordenadas Esféricas (r,q,f):
![Page 11: Coordenadas Curvilíneas](https://reader034.vdocuments.pub/reader034/viewer/2022051621/55cf8fed550346703ba15889/html5/thumbnails/11.jpg)
Gradiente de um Campo Escalar f(r,q,f):
Gradiente de um Campo Vetorial v(r,q,f):
Coordenadas Esféricas
![Page 12: Coordenadas Curvilíneas](https://reader034.vdocuments.pub/reader034/viewer/2022051621/55cf8fed550346703ba15889/html5/thumbnails/12.jpg)
Divergente de um Campo Vetorial v(r,q,f):
Divergente de um Campo Tensorial T(r,q,f):
Coordenadas Esféricas
![Page 13: Coordenadas Curvilíneas](https://reader034.vdocuments.pub/reader034/viewer/2022051621/55cf8fed550346703ba15889/html5/thumbnails/13.jpg)
Laplaciano de um Campo Escalar f(r,q,f):
Coordenadas Esféricas
![Page 14: Coordenadas Curvilíneas](https://reader034.vdocuments.pub/reader034/viewer/2022051621/55cf8fed550346703ba15889/html5/thumbnails/14.jpg)
Laplaciano de um Campo Vetorial v(r,q,f):
Coordenadas Esféricas
![Page 15: Coordenadas Curvilíneas](https://reader034.vdocuments.pub/reader034/viewer/2022051621/55cf8fed550346703ba15889/html5/thumbnails/15.jpg)
Obrigado pela atenção!