On the numerical integration of rigid body nonlinear dynamics in presence of parameters singularities

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 themselves, the body motion is well represented.

Narrative interviews: an important resource in qualitative research

Objetives This methodological study explain and emphasize the extent and fertility of the narrative interview in qualitative research. Methods To describe the narrative method within the qualitative research. Results The qualitative research method is characterized by addressing issues related to the singularities of the field and individuals investigated, being the narrative interviews a powerful method for use by researchers who aggregate it. They allow the deepening of research, the combination of life stories with socio-historical contexts, making the understanding of the senses that produce changes in the beliefs and values that motivate and justify the actions of possible informants. Conclusion The use of narrative is an advantageous investigative resource in qualitative research, in which the narrative is a traditional form of communication whose purpose is to serve content from which the subjective experiences can be transmitted.

Cultural singularities: indigenous elderly access to Public Health Service

OBJECTIVEDescribing how Kaingang seniors and their primary caregivers experience access to public health services.METHODA qualitative study guided by ethnography, conducted with 28 elderly and 19 caregivers. Data were collected between November 2010 and February 2013 through interviews and participative observation analyzed by ethnography.RESULTSThe study revealed the benefits and difficulties of the elderly access to health services, the facility to obtain health care resources such as appointments, medications and routine procedures, and the difficulties such as special assistance service problems and delays in the dispatching process between reference services.CONCLUSIONThe importance of knowing and understanding the cultural specificities of the group in order to offer greater opportunities for the elderly access to health services was reinforced.

Panel Method Formulation for Oscillating Airfoils in Sonic Flow

The mathematical model for two-dimensional unsteady sonic flow, based on the classical diffusion equation with imaginary coefficient, is presented and discussed. The main purpose is to develop a rigorous formulation in order to bring into light the correspondence between the sonic, supersonic and subsonic panel method theory. Source and doublet integrals are obtained and Laplace transformation demonstrates that, in fact, the source integral is the solution of the doublet integral equation. It is shown that the doublet-only formulation reduces to a Volterra integral equation of the first kind and a numerical method is proposed in order to solve it. To the authors' knowledge this is the first reported solution to the unsteady sonic thin airfoil problem through the use of doublet singularities. Comparisons with the source-only formulation are shown for the problem of a flat plate in combined harmonic heaving and pitching motion.