| Revista: | Journal of the Brazilian Society of Mechanical Sciences |
| Base de datos: | PERIÓDICA |
| Número de sistema: | 000312070 |
| ISSN: | 0100-7386 |
| Autores: | Trindade, Marcelo A1 Sampaio, Rubens |
| Instituciones: | 1Pontificia Universidade Catolica do Rio de Janeiro, Departamento de Engenharia Mecanica, Rio de Janeiro. Brasil |
| Año: | 2001 |
| Volumen: | 23 |
| Número: | 1 |
| Paginación: | 49-62 |
| País: | Brasil |
| Idioma: | Inglés |
| Tipo de documento: | Artículo |
| Enfoque: | Experimental |
| Resumen en inglés | One of the main complexities in the simulation of the nonlinear dynamics of rigid bodies consists in describing properly the finite rotations that they may undergo. It is well known that, to avoid singularities in the representation of the SO(3) rotation group, at least four parameters must be used. However, it is computationally expensive to use a four-parameters representation since, as only three of the parameters are independent, one needs to introduce constraint equations in the model, leading to differential-algebraic equations instead of ordinary differential ones. Three-parameter representations are numerically more efficient. Therefore, the objective of this paper is to evaluate numerically the influence of the parametrization and its singularities on the simulation of the dynamics of a rigid body. This is done through the analysis of a heavy top with a fixed point, using two three-parameter systems, Euler's angles and rotation vector. Theoretical results were used to guide the numerical simulation and to assure that all possible cases were analyzed. The two parametrizations were compared using several integrators. The results show that Euler's angles lead to faster integration compared to the rotation vector. An Euler's angles singular case, where representation approaches a theoretical singular point, was analyzed in detail. It is shown that on the contrary of what may be expected, 1) the numerical integration is very efficient, even more than for any other case, and 2) in spite of the uncertainty on the Euler's angles t |
| Disciplinas: | Matemáticas |
| Palabras clave: | Matemáticas puras, Rotaciones finitas, Angulos de Euler, Vector de rotación, Sistemas no lineales, Dinámica de sistemas, Singularidades, Representación |
| Keyword: | Mathematics, Pure mathematics, Finite rotations, Euler angles, Rotation vector, Nonlinear systems, System dynamics, Singularities, Representation |
| Texto completo: | Texto completo (Ver HTML) |
