Nonlinear dynamics and control of multibody systems

The dynamics of flexible systems, such as robot manipulators , mechanical chains or multibody systems in general, is becoming increasingly important in engineering. This article deals with some nonlinearities that arise in the study of dynamics and control of multibody systems in connection to large rotations. Specifically, a numerical scheme that adresses the conservation of fundamental constants is presented in order to analyse the control-structure interaction problems.

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.

A brief review and a new treatment for rigid bodies collision models

In general the motion of a body takes place in a confined environment and collision of the body with the containing wall is possible. In order to predict the dynamics of a body in this condition one must know what happens in a collision. Therefore, the problem is: if one knows the pre-collision dynamics of the body and the properties of the body and the wall one wants to predict the post-collision dynamics. This problem is quite old and it appeared in the literature in 1668. Up to 1984 it seemed that Newton's model was enough to solve the problem. But it was found that this was not the case and a renewed interest in the problem appeared. The aim of this paper is to treat the problem of plan collisions of rigid bodies, to classify the different models found in the literature and to present a new model that is a generalization of most of these models.

Interaction between the mineral content and the occurrence number of aquatic fungi in leaves submerged in a stream in the Atlantic rainforest, São Paulo, Brazil

Leaves of Ficus microcarpa L. f., Quercus robur L., and Alchornea triplinervia (Spreng.) Muell. Arg., submerged in a stream of the Atlantic rainforest in the "Reserva Biológica do Alto da Serra de Paranapiacaba", State of São Paulo, Brazil, were collected monthly, from April to November 1990, in order to determine the number of fungal occurrences (zoosporic fungi and aquatic Hyphomycetes), and the content of total N (%), total P (%), K+ (%), Ca+2 (%), Mg+2 (%), S+3 (%), Fe+3 (ppm), Cu+3 (ppm), Mn+2 (ppm), Zn+2 (ppm), Bo (ppm), Na+2 (ppm) and Al+3 (ppm). According to the tests of Kruskal-Wallis, Mann-Whitney and Wilcoxon, the means of the mineral content of the three types of leaves were significantly different, except for Mg+2 (%), Mn+2 (ppm), Zn+2 (ppm) and Na+2 (ppm). On comparing the mineral content with the number of fungal occurrence, an independence test showed a positive correlation between the presence of zoosporic fungi on the leaves of A. triplinervia and the total nitrogen, phosphorus and S+3 content, whereas the aquatic Hyphomycetes depended on the amount of Ca+2 available. Regarding leaves of F. microcarpa, the occurrence of zoosporic fungi was linked to the S+3 level, and the presence of aquatic Hyphomycetes, to the content of K+, Ca+2, S+3 and Bo. On Q. robur leaves, zoosporic fungi showed a positive correlation with the Ca+2 content, but a negative one with Fe+3 and Al+3 levels, while the occurrence of aquatic Hyphomycetes was influenced by the content of Ca+2, Mg+2, Fe+3, Al+3, Mn+2, Zn+2 and Na+2. The correlation between the occurrence number of aquatic Hyphomycetes and a high mineral content indicates that their nutritional requirements may be more complex than those of zoosporic fungi. Further studies are still required to understand the implications of this tendency on the diversity of aquatic native mycota.

Efeito do fósforo na captação de minerais e pigmentação de Azolla caroliniana Willd. (Azollaceae)

O bioacúmulo de minerais, a fixação de nitrogênio e a concentração de pigmentos em Azolla caroliniana foram estabelecidos sob estresse nutritivo. As culturas foram mantidas em frascos de poliestireno, utilizando gradiente de fosfato entre 10-7 e 10-3 mol.L-1. Os minerais (P, S, B e Sn) foram quantificados por espectrometria de emissão ótica com plasma de acoplamento induzido e o teor de nitrogênio pelo método de Kjeldahl. A atividade da nitrogenase foi determinada pela reação de redução do acetileno e as concentrações de pigmentos foram determinadas por fotometria nos extratos metanólicos acidificados. A absorção de macronutrientes (N, P, S) mostrou-se relacionada ao suprimento de fósforo, enquanto a absorção de micronutrientes (B e Sn) não sofreu este efeito. A seletividade mineral demonstra a potencialidade da A. caroliniana como biofertilizante. Para concentrações de fósforo abaixo de 10-5mol.L-1, a razão das clorofilas/antocianinas diminuiu, causando o avermelhamento do vegetal. Este comportamento de A. caroliniana poderia ser empregado para o biomonitoramento da disponibilidade de fósforo no ambiente.

Plant species and habitat structure in a sand dune field in the brazilian Caatinga: a homogeneous habitat harbouring an endemic biota

One dune habitat in the semi-arid Caatinga Biome, rich in endemisms, is described based on plant species composition, woody plant density, mean height and phenology and a multivariate analysis of the micro-habitats generated by variables associated to plants and topography. The local flora is composed mainly by typically sand-dweller species of Caatinga, suggesting the existence of a phytogeographic unity related to the sandy areas in the Caatinga biome, which seems to be corroborated by faunal distribution. Moreover, some species are probably endemic from the dunes, a pattern also found in vertebrates. The plant distribution is patchy, there is no conspicuous herbaceous layer and almost 50% of the ground represents exposed sand. Phenology is not synchronized among species, occurring leaves budding and shedding, flowers development and anthesis, fruits production and dispersion both in rainy and dry seasons. Leaf shedding is low compared to the level usually observed in Caatinga areas and about 50% of the woody individuals were producing leaves in both seasons. Spectrum of dispersal syndromes shows an unexpected higher proportion of zoochorous species among the phanerophytes, accounting for 31.3% of the species, 78.7% of the total frequency and 78.6% of the total density. The habitat of the dunes is very simple and homogeneous in structure and most of environmental variance in the area is explained by one gradient of woody plants density and another of increase of Bromelia antiacantha Bertol. (Bromeliaceae) and Tacinga inamoena (K. Schum.) N.P. Taylor & Stuppy (Cactaceae) toward valleys, which seem to determine two kinds of protected micro-habitats for the small cursorial fauna.

Dinâmica da comunidade e populações arbóreas da borda e interior de um remanescente florestal na Serra da Mantiqueira, Minas Gerais, em um intervalo de cinco anos (1999-2004)

A dinâmica da comunidade arbórea e de 26 populações componentes foi investigada em um fragmento de floresta estacional semidecídua em Piedade do Rio Grande, Minas Gerais, com base em inventários conduzidos em 1999 e 2004 em 30 parcelas de 400 m², 12 das quais foram locadas na borda do fragmento e 18 em seu interior. O objetivo foi verificar se a comunidade e populações arbóreas (a) estavam estáveis no período, e (b) mostraram uma dinâmica mais acelerada na borda do fragmento que em seu interior. Foram obtidas taxas de mortalidade e recrutamento de árvores e taxas de ganho e perda de área basal para a amostra total, seus dois setores, classes de diâmetro e populações. A hipótese da estabilidade foi rejeitada porque, tanto na borda como no interior, as taxas de mortalidade superaram as de recrutamento, as taxas de ganho superaram as de perda de área basal e as distribuições de tamanho mudaram devido ao declínio na densidade de árvores menores. Tais mudanças gerais se relacionaram, possivelmente, (a) a efeitos de longa duração da fragmentação ainda em curso, (b) a uma fase particular de um ciclo florestal rítmico e/ou (c) à suposta aceleração global das taxas de rotatividade florestal devido ao aumento do CO2 atmosférico. Os dois setores de fato diferiram nas taxas de rotatividade mais elevadas na borda que no interior da floresta, provavelmente devido à maior abundância de luz na borda, mas também porque populações de espécies pioneiras e exigentes de luz, de rápido crescimento, são mais abundantes na borda.

Reproductive phenology, pollination and seed dispersal syndromes on sandstone outcrop vegetation in the "Chapada Diamantina", northeastern Brazil: population and community analyses

Vegetation on rock outcrops in the "Chapada Diamantina" (soil islands) is often aggregated and surrounded by nude rock surfaces, thus creating natural units with well defined limits. The flowering and fruiting cycles of plants on 58 soil islands at altitudes between 1,100 and 1,140 meters above sea leavel were analyzed at Mãe Inácia Peak (12°27' S and 41°28' W) in the "Chapada Diamantina", Bahia, Brazil. The presence/absence of flowering and fruiting species on each soil island, and their respective cover areas were analyzed at both the population and community levels, and the phenophases of flowering and fruiting were observed during 24 successive months. The analyses of pollination and seed dispersal syndromes indicated that animals are more important in pollination than in seed dispersal (which is predominantly by anemochory and autochory). The flowering and fruiting of plants with animal pollination syndromes were correlated with rainfall and temperature. The flowering season varied during the year according to the pollination syndrome involved: entomophily was predominant from summer through autumn, ornithophily was predominant during winter, and anemophily in the spring. The staggered timing of flowering and fruiting among different species provides a nearly continuous supply of resources for the local fauna.

Floristics, structure and soil of insular vegetation in four quartzite-sandstone outcrops of "Chapada Diamantina", Northeast Brazil

Soil islands on rocky surfaces often harbor aggregated vegetation that consists of insular plant communities. These islands are typical of the rocky outcrops and in various parts of Brazil form the so-called "campos rupestres" vegetation. Four of such sites have been selected in the state of Bahia, Northeast Brazil, for this comparative study on floristics and vegetation structure: three areas situated inside the "Parque Nacional da Chapada Diamantina" (Guiné, Fumaça and "Gerais da Fumaça") and one is at the border of the Environmental Protection Area of "Marimbus-Iraquara" ("Mãe Inácia"). All occurring vegetation islands were studied in four random plots of 10 × 10 m per site. Soil was often shallow, sandy and acidic. Vascular plant species were determined, with respective life forms and canopy coverage areas. The total number of species when all four sites were added was 135, and the number of species per island varied from 2 to 32. The areas of the 214 soil islands varied from 0.015 to 91.9 m², totaling 568 m² in the four sites. Monocotyledon families were dominant, essentially Velloziaceae, as well as Orchidaceae, Bromeliaceae, Amaryllidaceae and Cyperaceae. Among the eudicotyledons, dominant families were mainly Clusiaceae, Asteraceae and Melastomataceae. The biological spectra revealed that phanerophytes and hemicryptophytes predominated among the life forms, while chamaephytes had the largest coverage area. Epilithic and desiccant chamaephytes composed the most conspicuous interspecific associations, and were probably related to early successional processes. Sites closest to one another were not the most similar in structure, indicating that other factors more relevant than distance might be involved in the abundance of species in space.

Padrões de distribuição geográfica das espécies de Schefflera J. R. Forst. & G. Forst. (Araliaceae) do Brasil extra-amazônico

Uma análise da distribuição geográfica de Schefflera no Brasil extra-amazônico foi realizada com base em mapas atualizados plotando as ocorrências conhecidas das 26 espécies do gênero encontradas nessa grande área: S. angustissima (Marchal) Frodin, S. aurata Fiaschi, S. botumirimensis Fiaschi & Pirani, S. burchellii (Seem.) Frodin & Fiaschi, S. calva (Cham.) Frodin & Fiaschi, S. capixaba Fiaschi, S. cephalantha (Harms) Frodin, S. cordata (Taub.) Frodin & Fiaschi, S. distractiflora (Harms) Frodin, S. fruticosa Fiaschi & Pirani, S. gardneri (Seem.) Frodin & Fiaschi, S. glaziovii (Taub.) Frodin & Fiaschi, S. grandigemma Fiaschi, S. kollmannii Fiaschi, S. longipetiolata (Pohl ex DC.) Frodin & Fiaschi, S. lucumoides (Decne. & Planch. ex Marchal) Frodin & Fiaschi, S. macrocarpa (Cham. & Schltdl.) Frodin, S. malmei (Harms) Frodin, S. morototoni (Aubl.) Maguire, Steyermark & Frodin, S. racemifera Fiaschi & Frodin, S. ruschiana Fiaschi & Pirani, S. selloi (Marchal) Frodin & Fiaschi, S. succinea Frodin & Fiaschi, S. villosissima Fiaschi & Pirani, S. vinosa (Cham. & Schltdl.) Frodin & Fiaschi e S. aff. varisiana Frodin. Dois centros de endemismo associados com áreas de altitude elevada foram reconhecidos: Cadeia do Espinhaço em Minas Gerais e florestas montanas do Estado do Espírito Santo. Os padrões de distribuição geográfica ilustrados são discutidos com base em dados obtidos para outros grupos de angiospermas e em estudos fitogeográficos das principais fitocórias do Brasil extra-amazônico. São apresentadas também hipóteses acerca de prováveis relações filogenéticas entre alguns táxons, visando à busca de possíveis correlações entre estas e a biogeografia do grupo.

A contribution to the phytogeography of Brazilian campos: an analysis based on Poaceae

Twenty areas from eight Brazilian states were compared according to a list of 224 species of Poaceae. In order to determinate affinity patterns between the areas, a binary matrix was submitted to cluster and ordination analysis. The patterns found were then faced to climate and geographic position. The scores corresponding to the areas obtained from the cluster analysis showed a strong correlation to temperature. The scores corresponding to the species suggest a gradient that associates distribution patterns to the photosynthetic pathway (C3 or C4). The current results suggest that the traditional classification of the Southern American grasslands might require some modification in order to be broadly applicable in the Brazilian context.

Morfoanatomia da flor de cinco espécies de Galipea Aubl. e seu significado na evolução de flores tubulosas entre as Rutaceae neotropicais

A maioria dos gêneros da subtribo neotropical Galipeinae (tribo Galipeeae, Rutoideae) tem flores tubulosas, com várias formas e graus de conação e adnação. Galipea e outros gêneros na subtribo apresentam apenas duas anteras férteis mais cinco ou mais estaminódios, o que é intrigante porque na tribo predominam flores pentâmeras isostêmones. Visando elucidar a condição anatômica dessas características e estabelecer estados acurados para caracteres em análises filogenéticas, um estudo morfoanatômico de flores de cinco espécies de Galipea foi realizado, buscando os padrões de vascularização, posição, e união dos segmentos da flor. Destacam-se os resultados: 1) um tubo floral genuíno se forma no terço basal da flor por conação dos filetes e adnação desse tubo estaminal às pétalas; 2) as pétalas são distalmente coerentes umas às outras e aderentes aos filetes por meio de entrelaçamento de tricomas densos - um caso de pseudossimpetalia; 3) dentre as cinco (às vezes seis) estruturas tratadas como estaminódios, apenas as três externas são de fato homólogas a estames esterilizados, as demais surgem como ramificações adaxiais das pétalas; 4) os carpelos são peltados, congenitalmente conatos axial e lateralmente da base do ovário até o nível das placentas, e no estilete e estigma; na zona mediana e superior do ovário eles são unidos apenas posgenitalmente, com a epiderme diferenciada de carpelos contíguos e suturas evidentes na região ventral de cada carpelo; 5) a vascularização do disco sugere origem receptacular. As implicações desses dados para o entendimento da evolução das flores tubulosas em Galipea e grupos relacionados são discutidas.

Padrões de distribuição geográfica das espécies de Chamaecrista sect. Chamaecrista ser. Coriaceae (Benth.) H. S. Irwin & Barneby, Leguminosae - Caesalpinioideae

Uma análise de distribuição geográfica de Chamaecrista sect. Chamaecrista ser. Coriaceae foi realizada com base em mapas atualizados plotando as ocorrências conhecidas de 27 táxons (20 espécies) da série. Apenas uma espécie ocorre na região do Caribe, nas Bahamas, C. caribaea (Northr.) Britton, enquanto todas as demais estão presentes no principal centro de diversidade, a Cadeia do Espinhaço, exibindo dois padrões principais: 1) ocorrência contínua ou disjunta ao longo da Cadeia do Espinhaço e áreas adjacentes ou disjuntas e 2) espécies endêmicas da porção sul dessa formação montanhosa. Entre as disjunções, destacam-se três espécies, uma ocorrendo no Espinhaço e em serras do "Arco de Brasília" até Goiás (C. cardiostegia H. S. Irwin & Barneby), uma no Espinhaço e no Espírito Santo (C. mucronata (C. Sprengel) H. S. Irwin & Barneby) e outra centrada no Espinhaço e no Planalto das Guianas (C. roraimae (Benth.) Gleason). Os padrões de distribuição geográfica são discutidos com base em dados obtidos sobre outros grupos de angiospermas e uma análise realizada anteriormente com cinco espécies da série. Os resultados demonstram uma concentração de espécies restrita a regiões de altitude situadas no Domínio do Cerrado, corroborando o alto grau de endemismo já documentado em outros grupos na região. Essa análise constitui um primeiro passo para possibilitar estudos visando à compreensão dos processos responsáveis pela diversificação do grupo no cerrado, sobretudo em áreas elevadas.

Application of the Hsu model to soybean grain hydration

A comparative analysis of the theoretical-experimental study, developed by Hsu on the hydration of Amsoy 71 soybean grain, was performed through several soaking experiments using CD 202 soybean at 10, 20, 30, 40, and 50 °C, measuring moisture content over time. The results showed that CD 202 soybean equilibrium moisture content, Xeq, does not depend on temperature and is 21% higher than that found by Hsu, suggesting that soybean cultivar exerts great influence on Xeq. The Hsu model was numerically solved and its parameters were adjusted by the least squares method, with maximum deviations of +/- 10% relative to the experimental values. The limiting step in the mass transfer process during hydration corresponds to water diffusion inside the grain, leading to radial moisture gradients that decrease over time and with an increase in temperature. Regardless of the soybean cultivar, diffusivity increases as temperature or moisture content increases. However, the values of this transport property for Amsoy 71 were superior to those of CD 202, very close at the beginning of hydration at 20 °C and almost three times higher at the end of hydration at 50 °C.

Cadmium determination in Lentinus edodes mushroom species

Many studies have drawn attention to the occurrence and concentration of toxic elements found in the fruiting body of mushrooms. Some edible mushroom species are known to accumulate high levels of inorganic contaminants, mainly cadmium, mercury, and lead. There are about 2,000 known edible mushroom species, but only 25 of them are cultivated and used as food. In Brazil, the most marketed and consumed mushroom species are Agaricus bisporus, known as Paris champignon, Lentinus edodes, or Shitake and Pleurotus sp, also called Shimeji or Hiratake. In this study, the concentration of cadmium was determined in Lentinus edodes mushrooms from different cities in São Paulo state and some samples imported from Japan and China. The analyses were performed by graphite furnace atomic absorption spectrometry after HNO3-H2O2 digestion. The results showed a lower concentration of Cd in the mushrooms cultivated in São Paulo (0.0079 to 0.023 mg.kg-1 in natura) than that of the mushrooms cultivated abroad (0.125 to 0.212 mg.kg-1 in natura). Although there is no tolerance limit for Cd in mushrooms in Brazil, the results show that Lentinus edodes mushrooms can be safely consumed.