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.

Analysis of Regular and Irregular Dynamics of a Non Ideal Gear Rattling Problem

This paper presents a study on the dynamics of the rattling problem in gearboxes under non-ideal excitation. The subject has being analyzed by a number of authors such as Karagiannis and Pfeiffer (1991), for the ideal excitation case. An interesting model of the same problem by Moon (1992) has been recently used by Souza and Caldas (1999) to detect chaotic behavior. We consider two spur gears with different diameters and gaps between the teeth. Suppose the motion of one gear to be given while the motion of the other is governed by its dynamics. In the ideal case, the driving wheel is supposed to undergo a sinusoidal motion with given constant amplitude and frequency. In this paper, we consider the motion to be a function of the system response and a limited energy source is adopted. Thus an extra degree of freedom is introduced in the problem. The equations of motion are obtained via a Lagrangian approach with some assumed characteristic torque curves. Next, extensive numerical integration is used to detect some interesting geometrical aspects of regular and irregular motions of the system response.

On non-ideal and non-linear portal frame dynamics analysis using bogoliubov averaging method

We apply the Bogoliubov Averaging Method to the study of the vibrations of an elastic foundation, forced by a Non-ideal energy source. The considered model consists of a portal plane frame with quadratic nonlinearities, with internal resonance 1:2, supporting a direct current motor with limited power. The non-ideal excitation is in primary resonance in the order of one-half with the second mode frequency. The results of the averaging method, plotted in time evolution curve and phase diagrams are compared to those obtained by numerically integrating of the original differential equations. The presence of the saturation phenomenon is verified by analytical procedures.

Market integration, return and volatility dynamics; empirical evidence from African stock markets

Frontier and Emerging economies have implemented policies with the objective of liberalizing their equity markets. Equity market liberalization opens the domestic equity market to foreign investors and as well paves the way for domestic investors to invest in foreign equity securities. Among other things, equity market liberalization results in diversification benefits. Moreover, equity market liberalization leads to low cost of equity capital resulting from the lower rate of return by investors. Additionally, foreign and local investors share any potential risks. Liberalized equity markets also become liquid considering that there are more investors to trade. Equity market liberalization results in financial integration which explains the movement of two markets. In crisis period, increased volatility and co-movement between two markets may result in what is termed contagion effects. In Africa, major moves toward financial liberalization generally started in the late 1980s with South Africa as the pioneer. Over the years, researchers have studied the impact of financial liberalization on Africa’s economic development with diverse results; some being positive, others negative and still others being mixed. The objective of this study is to establish whether African stock-markets are integrated into the United States (US) and World market. Furthermore, the study helps to see if there are international linkages between the Africa, US and the world markets. A Bivariate- VAR- GARCH- BEKK model is employed in the study. In the study, the effect of thin trading is removed through series of econometric data purification. This is because thin trading, also known as non-trading or inconsistency of trading, is a main feature of African markets and may trigger inconsistency and biased results. The study confirmed the widely established results that the South Africa and Egypt stock markets are highly integrated with the US and World market. Interestingly, the study adds to knowledge in this research area by establishing the fact that Kenya is very integrated with the US and World markets and that it receives and exports past innovations as well as shocks to and from the US and World market.

Germination and emergence of Stachytarpheta cayennensis and Ipomoea asarifolia

Understanding how weed seed germination and emergence respond to environmental factors is critical to determining their adaptive capabilities and potential for infestations, and could also aid in the development of effective control practices. Germination of Ipomoea asarifolia (Desr.) Roem. & Schultz and Stachytarpheta cayennensis (Rich) Vahl. decreased linearly with decreasing osmotic potentials. Also, increasing osmotic stress delayed germination of Ipomoea more than that of Stachytarpheta. Ipomoea germination was insensitive to light, while Stachytarpheta showed a positive photoblastic behavior. Nitrate had a negative effect on germination of Ipomoea seed under both light and dark conditions but stimulated dark germination of Stachytarpheta. Ipomoea emergence was not significantly affected by planting depth. However, for Stachytarpheta emergence was restrited to seeds planted at the soil surface. Emergence of Ipomoea seedlings from greater than 6cm significantly decreased the amount of biomass allocated to roots, while biomass allocated to leaves was decreased for seedlings that emerged from depths greater than 2cm. These germination and emergence responses are discussed in relation to their ecological implications and to weed control strategies.

Mathematics inspired by Darwin. Adaptive dynamics of dispersal and cooperation

In 1859, Charles Darwin published his theory of evolution by natural selection, the process occurring based on fitness benefits and fitness costs at the individual level. Traditionally, evolution has been investigated by biologists, but it has induced mathematical approaches, too. For example, adaptive dynamics has proven to be a very applicable framework to the purpose. Its core concept is the invasion fitness, the sign of which tells whether a mutant phenotype can invade the prevalent phenotype. In this thesis, four real-world applications on evolutionary questions are provided. Inspiration for the first two studies arose from a cold-adapted species, American pika. First, it is studied how the global climate change may affect the evolution of dispersal and viability of pika metapopulations. Based on the results gained here, it is shown that the evolution of dispersal can result in extinction and indeed, evolution of dispersalshould be incorporated into the viability analysis of species living in fragmented habitats. The second study is focused on the evolution of densitydependent dispersal in metapopulations with small habitat patches. It resulted a very surprising unintuitive evolutionary phenomenon, how a non-monotone density-dependent dispersal may evolve. Cooperation is surprisingly common in many levels of life, despite of its obvious vulnerability to selfish cheating. This motivated two applications. First, it is shown that density-dependent cooperative investment can evolve to have a qualitatively different, monotone or non-monotone, form depending on modelling details. The last study investigates the evolution of investing into two public-goods resources. The results suggest one general path by which labour division can arise via evolutionary branching. In addition to applications, two novel methodological derivations of fitness measures in structured metapopulations are given.

Seletividade de herbicidas aplicados em pós-emergência sobre capim-colonião e efeito na qualidade das sementes: effects on seed germination

Este estudo foi conduzido para avaliar a seletividade de herbicidas aplicados em pós-emergência sobre plantas de Panicum maximum, cultivares Tanzânia e Mombaça, e os seus efeitos na qualidade das sementes. Os tratamentos testados (em g ha-1) foram: diclofopmethyl (284), ametryne (1.250), propanil (3.600), chlorimuron-ethyl (15), nicosulfuron (50), bentazon (720) e atrazine (3.000), além de uma testemunha sem aplicação de herbicidas. Foram instalados dois experimentos a campo, um para cada cultivar, no delineamento em blocos casualizados com quatro repetições, e um em laboratório, no delineamento inteiramente casualizado, com 16 repetições. O nicosulfuron foi o herbicida que mais causou injúrias visuais e redução de massa seca de plantas em ambos os cultivares. No cultivar Mombaça, todos os herbicidas reduziram a produção de sementes, mas não afetaram a germinação. Para o cultivar Tanzânia, todos os herbicidas foram seletivos, não afetando a produção e a qualidade fisiológica.

Influence of environmental factors on seed germination and seedling emergence of yellow sweet clover (Melilotus officinalis)

Laboratory and greenhouse experiments were conducted to determine the effects of drought and salinity stress, temperature, pH and planting depth on yellow sweet clover (Melilotus officinalis) germination and emergence. Base, optimum and ceiling germination temperatures were estimated as 0, 18.47 and 34.60 ºC, respectively. Seed germination was sensitive to drought stress and completely inhibited at a potential of -1 MPa, but it was tolerant to salinity. Salinity stress up to 90 mM had no effect over the M. officinalis seed germination, but the germination decreased by increasing the salt concentration. The drought and salinity required for 50% inhibition of maximum germination were 207 mM and -0.49 MPa, respectively. High percentage of seed germination (>92%) was observed at pH = 5-6 and decreased to 80% at acidic medium (pH 4) and to 42% at alkaline medium (pH 9) pH. Maximum seedling emergence occurred when the seeds were placed at 2 cm depth and decreased when increasing the depth of planting; no seed emerged from depths of 10 cm.

Effect of crop residues applied isolated or in combination on the germination and seedling growth of horse purslane (Trianthema portulacastrum)

Soil incorporation of crop residues can lead to weed suppression by posing allelopathic and physical effects. Allelopathic potential of the crops sorghum, sunflower, brassica applied as sole or in combination for horse purslane (Trianthema portulacastrum) suppression was evaluated in a pot investigation. Chopped crop residues alone and in combination were incorporated at 6 g kg-1 soil (12 t ha-1), and a weedy check was maintained. Germination traits time to start germination; time to 50% emergence, mean emergence time, emergence index and final germination percentage were negatively influenced by residue incorporation. Crop residues also exerted a pronounced negative influence on the shoot and root length of horse purslane. Significant suppression in leaf and root score and leaf area per plant was also observed. A combination of sorghum and sunflower residues accounted for maximum (71%) seedling mortality. Soil incorporation of allelopathic crop residues can be employed for horse purslane management.

Design and implementation of a production synchronization extension for Microsoft Dynamics AX

In a just-in-time, assemble-to-order production environments the scheduling of material requirements and production tasks - even though difficult - is of paramount importance. Different enterprise resource planning solutions with master scheduling functionality have been created to ease this problem and work as expected unless there is a problem in the material flow. This case-based candidate’s thesis introduces a tool for Microsoft Dynamics AX multisite environment, that can be used by site managers and production coordinators to get an overview of the current open sales order base and prioritize production in the event of material shortouts to avoid part-deliveries.

School Bullies’ Quest for Power: Implications for Group Dynamics and Intervention

Bullying is characterized by an inequality of power between perpetrator and target. Findings that bullies can be highly popular have helped redefine the old conception of the maladjusted school bully into a powerful individual exerting influence on his peers from the top of the peer status hierarchy. Study I is a conceptual paper that explores the conditions under which a skillful, socially powerful bully can use the peer group as a means of aggression and suggests that low cohesion and low quality of friendships make groups easier to manipulate. School bullies’ high popularity should be a major obstacle for antibullying efforts, as bullies are unlikely to cease negative actions that are rewarding, and their powerful position could discourage bystanders from interfering. Using data from the Finnish program KiVa, Study II supported the hypothesis that antibullying interventions are less effective with popular bullies in comparison to their unpopular counterparts. In order to design interventions that can address the positive link between popularity and aggression, it is necessary to determine in which contexts bullies achieve higher status. Using an American sample, Study III examined the effects of five classroom features on the social status that peers accord to aggressive children, including classroom status hierarchy, academic level and grade level, controlling for classroom mean levels of aggression and ethnic distribution. Aggressive children were more popular and better liked in fifth grade relative to fourth grade and in classrooms of higher status hierarchy. Surprisingly, the natural emergence of status hierarchies in children’s peer groups has long been assumed to minimize aggression. Whether status hierarchies hinder or promote bullying is a controversial question in the peer relations’ literature. Study IV aimed at clarifying this debate by testing the effects of the degree of classroom status hierarchy on bullying. Higher hierarchy was concrrently associated with bullying and predictive of higher bullying six months later. As bullies’ quest for power is increasingly acknowledged, some researchers suggest teaching bullies to attain the elevated status they yearn for through prosocial acts. Study V cautions against such solutions by reviewing evidence that prosocial behaviors enacted with the intention of controlling others can be as harmful as aggression.

Influence of seed size and ecological factors on the germination and emergence of field bindweed (Convolvulus arvensis)

An understanding of seed germination ecology of weeds can assist in predicting their potential distribution and developing effective management strategies. Influence of environmental factors and seed size on germination and seedling emergence of Convolvulus arvensis (field bindweed) was studied in laboratory and greenhouse conditions. Germination occurred over a wide range of constant temperatures, between 15 and 40 ºC, with optimum germination between 20 and 25 ºC. Time to start germination, time to 50% germination and mean germination time increased while germination percentage and germination index decreased with an increase in temperature from 20 ºC, salinity and osmotic stress. However, germination was tolerant to low salt (25 mM) or osmotic stress (0.2 MPa), but as salinity and osmotic stress increased, germination percentage and germination index decreased. Seeds of C. arvensis placed at soil surface showed maximum emergence and decreased as seeding depth increased. Seeds of C. arvensis germinated over a wide range of pH (4 to 9) but optimum germination occurred at pH 6 to 8. Under highly alkaline and acidic pH, time to start germination, time to 50% germination and mean germination time increased while germination percentage and germination index decreased. Increase in field capacity caused decreased time to start germination, time to 50% germination and mean germination time but increased germination percentage and germination index. Bigger seeds had low time to start germination, time to 50% germination and mean germination time but high germination percentage and germination index. Smaller seeds were more sensitive to environmental factors as compared to larger or medium seeds. It can be concluded that except for pH, all environmental factors and seed sizes adversely affect C. arvensis as regards seed germination or emergence and germination or emergence traits, and larger seeds result in improved stand establishment and faster germination than small seeds, regardless of moisture stress or deeper seeding depth.

Germination ecology of Rhynchosia capitata: an emerging summer weed in Asia

Rhynchosia capitata is becoming an increasing problem in summer crops, such as cotton, soybean, pearl millet and mungbean in many Asian countries. Laboratory and greenhouse studies have been conducted to determine the effects of several environmental factors on seed germination patterns and seedling emergence of R. capitata. We investigated whether the diverse ecological factors such as temperature, light, salinity, moisture stress, pH, and soil depth affected germination and seedling emergence of R. capitata. Germination increased as temperature increased from 25ºC and significantly reduced at 45ºC. Presence or absence of light did not influence germination. Germination of R. capitata was sensitive to increased salt and moisture stress, as well as to seed burial depth. Only 48% of seeds germinated at 150 mM salt concentration compared to 100% in control (distilled water). Similarly, 15% of seeds germinated at an osmotic potential of ‑0.8 MPa compared to 88% at ‑0.2 MPa. The optimum pH for seed germination of R. capitata was 7 (98% germination), but the seeds also germinated at lower level of pH 5 (85%) and at higher level of pH 10 (75%). In seed burial trial, maximum seedling emergence of 93% occurred at 2 cm depth, and seedling did not emerge from a depth of 12 cm. The high germination ability of R. capitata under a wide range of ecological factors suggests that this species is likely to be the one to cause more problems in a near future, if not managed appropriately.

Seed germination and seedling emergence of velvetleaf (Abutilon theophrasti) and Barnyardgrass (Echinochloa crus-galli)

Abutilon theophrasti and Barnyardgrass (Echinochloa crus-galli) are major weeds that affect cropping systems worldwide. Laboratory and greenhouse studies were conducted to determine the effects of temperature, pH, water and salinity stress, and planting depth on seed germination and seedling emergence of Velvetleaf and Barnyardgrass. For Velvetleaf, the base, optimum and ceiling germination temperatures were estimated as 5, 35 and 48 ºC, respectively. Seed germination was sensitive to drought stress and completely inhibited by a potential of -0.6 MPa, but it was tolerant to salinity. Salinity stress up to 45 mM had no effect on the germination of Velvetleaf, but germination decreased with increasing salt concentration. Drought and salinity levels for 50% inhibition of maximum germination were -0.3 MPa and 110 mM, respectively. Seed germination of Velvetleaf was tolerant to a wide range of pH levels. For Barnyardgrass, the base, optimum and ceiling germination temperatures were estimated as 5, 38 and 45 ºC, respectively. Seed germination was tolerant to drought stress and completely inhibited by a potential of -1.0 MPa. Salinity stress up to 250 mM had no effect on seed germination. Drought and salinity levels for 50% inhibition of maximum germination were -0.5 MPa and 307 mM, respectively. A high percentage of seed germination was observed at pH=5 and decreased to 61.5% at acidic medium (pH 4) and to 11% at alkaline medium (pH 9). Maximum seedling emergence of Velvetleaf and Barnyardgrass occurred when the seeds were placed on the surface of the soil or at a depth of 1 cm.