Transformações Geométricas no Plano e no Espaço

• Ano de defesa: 2013
• Autor(a) principal: Silva, Rênad Ferreira da
• Tipo de documento: Dissertação
• Tipo de acesso: Acesso aberto
• Idioma: por
• Instituição de defesa: Universidade Federal da Paraíba; Brasil; Matemática; Mestrado Profissional em Matemática; UFPB
• Palavras-chave em Português: Transformações Geométricas; Geometric Transformations; Ângulos de Euler; Grupo dos Quatérnios; Espaço Homogêneos; Angles of Euler; Quaternions Groups; Homogeneous Space; MATEMATICA::MATEMATICA APLICADA
• Link de acesso: https://repositorio.ufpb.br/jspui/handle/tede/7476

Abstract: In this work we study some geometric transformations in the plane and the space. Initially, we present some special types of transformations in the plane and find the matrix of each of these transformations. In the second part we discourse the transformations in the space, emphasizing the rotations. We will use the angles of Euler to determine a rotation in the space around the Cartesian axes and define an equation which allows to rotate a vector around any axis. We also discuss the homogeneous spaces aiming the matrix representation of transformations of translation. Finally, we use the structure of the quaternions group to present a second form to rotation vectors and composition of rotations in the space. We emphasize that this study is essential to describe the motion of objects in the plane and in the space.