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AbstractHamiltonian system is a special case of dynamical system. Mostly it is used for potential shaping of mechanical systems stabilization. In our present work, we are using Hamiltonian dynamics to study and control the fuel slosh inside spacecraft tank. Sloshing is the phenomenon which is related with the movement of fluid inside a container in micro and macro scale as well. Sloshing of fluid occurs whenever the frequency of container movement matches with the natural frequency of fluid inside the container. Such type of synchronization may cause the structural damage or could be a reason of moving object's attitude disturbance. In spacecraft technology, the equivalent mechanical model for sloshing is common to use for the representation of fuel slosh. This mechanical model may contain a model of pendulum or a mass attached with a spring. In this article, we are using mass-spring mechanical model coupled with rigid body to derive the equations for Hamiltonian system. Casimir functions are used for proposed model. Conditions for the stability and instability of moving mass are derived using Lyapunov function along with Casimir functions. Simulation work is presented to strengthen the derived results and to distribute the stable and unstable regions graphically.

AbstractTwo experiments were conducted over the 1995/96 and 1996/97 growing seasons, at Lincoln University and New Zealand Institute for Crop & Food Research, Lincoln, Canterbury to assess the effects of nitrogen and potato cyst nematode (Globodera rostocheinsis)on the development of early blight epidemics. The objective was to measure effects on photosynthetically active radiation (PAR) intercepted by crops under multiple pest constraints, and also to compare the effect of early blight, nitrogen, and potato cyst nematode on integrated values for healthy leaf area duration (HAD) and healthy leaf area absorption (HAA). Epidemic development of early blight was rapid in high nitrogen fertility plots and in plots with 30 nematode eggs/ml of soil in 1995/96, but in 1996/97 neither nitrogen nor potato cyst nematode significantly affected the epidemic development. In these trials the intercepted PAR (HAA) was derived from the integral over time of green leaf area index (GLAI) which was used as a measure of HAD. HAD and HAA were derived from leaf area index (LAI) corrected by two methods, the percent reflectance (PR) ratio or percent yellowing (PY). This paper explains the detailed correction methods used and shows that LAI corrected with PR ratio is the best way for calculating GLAI from a diseased crop, which can then be used for calculating HAA. Early blight and potato cyst nematode significantly reduced HAD and HAA whereas nitrogen significantly increased HAD and HAA in both growing seasons. The effect of disease on HAD and HAA was not altered by nitrogen or potato cyst nematode in both growing seasons.

AbstractFour experiments were conducted over two growing seasons during 1995/96 and 1996/97 at Lincoln University and New Zealand Institute for Crop & Food Research, Lincoln, Canterbury, to assess whether radiation interception (RI) alone is a good predictor of potato (Solanum tuberosum)total dry matter (TDM) grown under different environments. In the two field experiments production environments were altered by different rates of nitrogen application and in bag experiments, the different production environments were created with the presence of different amounts of potato cyst nematode (Globodera rostochiensis)per ml of soil. The different production environments significantly affected leaf area index (LAI), RI, radiation use efficiency (RUE), and TDM. Increased soil fertility significantly increased RI, RUE, and TDM where as the presence of potato cyst nematode significantly decreased RI, RUE, and TDM. There was a strong (P <0.001) positive linear relationship between RUE and applied nitrogen, whereas there was a linear, negative relationship between RUE and the numbers of potato cyst nematode per ml of soil. On the basis of this study it was concluded that under different production environments both RI and RUE must be known to accurately predict the TDM of potatoes.

AbstractFour experiments were conducted over two growing seasons during 1995/96 and 1996/97 at Lincoln University and the New Zealand Institute for Crop & Food Research, Lincoln, Canterbury. A large database was used to assess the effects of production environments on disease yield relationships and to compare different models derived from pathogen‐based disease measurement and host‐based disease measurements. All the models were developed using regression analyses. All the single point (SP), multiple point (MP), and integral models derived from host‐based disease measurements explained more variation than models derived from pathogen‐based disease measurements. SP, MP, and integral models were also compared and integral models were selected as the best for comparing disease effects as they combine the effect of disease over the whole growing season in one variable. Further, integral models were tested for the effect of different production environments on disease yield relationships. It was found that the nitrogen‐altered production environments had no significant effect on disease yield relationships, whereas potato cyst nematode‐altered production environments significantly affected the disease yield relationship. A single model was used for the disease yield relationship for nitrogen inputs, whereas separate disease yield relationships were used for each nematode level.