Non-integrability of a model of elastic dumbbell satellite

We study the integrability of a model of elastic satellite whose centre of mass moves in a circular Keplerian orbit around a gravity centre. The satellite is modelled by two point masses connected by an extensible massless spring that obeys Hooke’s law. It is assumed that the distance between point masses is much smaller than the radius of the orbit, so the orbital motion of the satellite is not perturbed by its rotational motion. The gravity potential of the satellite is expanded into a series with respect to its size up to quadratic terms which describe the gravity gradient torque acting on the satellite. Two cases are considered with Hooke’s centre localised in the centre of mass of the dumbbell and at an arbitrary point along a line connecting both masses. It is shown that the first case appears to be integrable and super-integrable for selected values of the parameter of the system. In the second case, model depends effectively only on one parameter and is non-integrable. In the proof, differential Galois integrability obstructions are used. For the considered sysem, these obstructions are deduced thanks to the recently developed symplectic Kovacic’s algorithm in dimension 4. According to our knowledge, this is the first application of this tool to a physical model.

Using the depth of the centre of gravity as an indicator on the state of the general ocean circulation

<p>An approach is here investigated that uses the depth of the centre of gravity as a central ocean property, thought to give a clear and practical indicator on the state of the general ocean circulation. The depth of the gravity centre can be directly linked to the volume-integral of potential energy, or of dynamic enthalpy when making the Boussinesq approximation, and therefore to the strength of the global mean stratification. Because the stratification is directly linked to the global overturning circulation, it is hypothesized that the depth of the centre of gravity can be used to assess the state of global circulation. In order to test this hypothesis, the depth of the centre of gravity is diagnosed in an ocean model simulation for an idealized square basin configuration with the NEMO model. The centre of gravity is compared to the value it would have if the ocean was perfectly well mixed, giving a state of maximum potential energy. We find in our idealized simulation that the centre of gravity is lowered by only 22 cm compared to the reference well-mixed state, reflecting the potential energy that would be required to destroy the ocean stratification. The smallness of that number highlights the inefficiency of the ocean engine. Furthermore, the dynamic balance setting the depth of the gravity centre is investigated, diagnosing separately the tendency terms on the equation of conservation of potential energy. A positive change (sinking) of the centre of gravity indicates an input of high density water into lower levels or low density water in upper levels, essentially enhancing the global mean stratification, while for a negative change (lifting) it is reversed. The goal is to compare the relative role of the wind stress, surface buoyancy forcing and internal mixing in setting the general circulation.</p>

Technology of steel jackets load-out in deep-water offshore platforms from the barge

Currently, great attention is paid to the development issue of the shelf’s fuel and energy resources foremost in the oil-gas fields of the Caspian Sea. The problem solution requires the studying of great majority of scientific-technical issues. One of the significant problems is the lead-out of steel jacket from the offshore platform as a major element of oil-gas field hydro-technical facilities meant for the operation in the deep water. The calculations for the execution of operations with steel jacket of deep stationary platform from the block with the detailed chara- cteristics by the mass and gravity center coordinates alongside line data have been carried out with “SACS” and “STAAD.PRO” software programs. The steel jacket is pushed astern with the push-pull equipment on the barge. Due to the shift of gravity centre the jacket changes the trim in the stern. Through the elevation of trim angle brought in alignment with the friction ration between the jacket and barge, the jacket slides further itself. Herewith, the trim increases until the gravity centre of steel jacket on the barge is not in alignment with rotation centre of the large rocker arms. The studies helped to fix the position of the jacket’s gravity centre from the aft perpendicular, the trim moment, the trim of the barge, the draft with the bow and stern and the trim angle as well.

Spatial Heterogeneity and Coupling of Economy and Population Gravity Centres in the Hengduan Mountains

The junction region of the Sichuan–Yunnan–Guizhou province (JRSYG) is a multinational community that includes the Hengduan mountainous areas, although its economy is lagging behind other regions in China. This study explored the spatial heterogeneity and coupling of economic and population gravity centres during the period 1995–2015, and determined the hotspots driving the economic development in the JRSYG region. We obtained the following results: (1) The global Moran’s I and the Moran scatter plots of the economy and population showed that the distribution of economy and population was a nature clustering. The scatter plots of the economy and population were mainly distributed in Quadrant III, with an L–L gathering. With the passage of time, the agglomeration and driving effects of the economy become stronger. (2) By the dynamic evolution process of the economy and population, the economy gravity centre (GE) and population gravity centre (GP) were approaching each other during the period 1995–2015. The equilibrium points showed an inverted U-shaped curve for the past few years. The spatial coupling of GE and GP increased every year. The balanced degree of regional development continuously improved. (3) The economic development level showed a polarisation pattern with a southwest growth pole and northeast growth pole. The point–axis spatial development pattern is presented, with two economic hotspots (Panzhihua and Luzhou) and three sub-hotspots (Xichang, Zhong shan, Zhaoyang). If further advantages from policy and infrastructure support are obtained, the hot poles can drive the social and economic development of the surrounding regions, which will alleviate regional differences in the future.

Turbine Blade of Gas Turbine Engine Additional Unloading by Changing the Layout of the Gravity Centre of the Shroud Shelf

The article describes the impact of the gas turbine engine low-pressure turbine blade shroud shelf on the blade profile stress position. Attention is focused directly on the impact of the location of the gravity centre of the shroud shelf on blade stress distribution at the three most critical points of the profile. The paper describes the details of the calculation and the required expressions provided, as well as the results of the calculation example with clear graphical dependencies.

RESISTANCE WHILE MANAGING ITS OWN INERTIAL POWER FIELD

The study of the managing methods represents particular interest in the biomechanics for the human body motor as well the opportunities for its improvement. (1) The basic problem related to the managing is to understand and to be aware of the task itself, the performance and the possibility for the reproduction. (2,3) Therefore the aim of this study is to try to determine the quantity of the basic parameters of the balanced resistance and also during the examination in order to influence the managing method. There were examined 85 individuals (33 women and 52 men) taking part in the test. The test battery includes performing of the supporting human body tasks on a stable graphic platform. The projections of the Gravity Centre have been studied and the task for the individuals submitted to the test is to manage the Gravity Center having their full conscience. During the performance a quantity difference has been observed and therefore we could establish the conclusions related to the degree of consciousness regarding the managing methods.