Symplectic Mappings of Co-orbital Motion in the Restricted Problem of Three Bodies

The dynamics of co-orbital motion in the restricted three-body problem are investigated by symplectic mappings. Analytical and semi-numerical mappings have been developed and studied in detail. The mappings have been tested by numerical integration of the equations of motion. These mappings have been proved to be useful for a quick determination of the phase space structure reflecting the main characteristics of the dynamics of the co-orbital problem.     

Problems in data compilation

Concepts involved in the estimation of target quantities and other adjustment parameters are critically discussd. We point out that one can find more accurate precepts for the reduction of data by utilizing all available constraints on all available data in the derivation of the reduction precepts. We introduce a measure for theefficiency of a set of adjustment parameters such that adjustments carried out using different precepts can be objectively compared. Finally, having applied our suggestions to a specific problem, we show that we have obtained estimates of a set of target quantities (in our case, star positions and proper motions) which have smaller formal errors than estimates of the same target quantities derived from the same input material but following traditional procedures.     

Evidence for a small,high-Z,iron-like solar core

Radial and nonradial oscillation equations without and with the gravitation perturbation (with and without the Cowling approximation, CA) are solved numerically using the profile from a more accurate high-Z core (HZC) solar model. This more accurate HZC model was generated with the CRAY X-MP/48 supercomputer at the San Diego Supercomputer Center. Frequencies of oscillation in the five-min band (5MB) and frequencies with period near 160 min are presented in tables and plotted in echelle diagrams. The model was generated by integrating the stellar structure equations from the center to he surface, as done in Rouse (1964), using a maximum space step, ;x _m = 5 × 10^–4, decreasing to 10^–6 in the hydrogenionization zone just below the photosphere. Two subsets of space mesh points are used to calculate the oscillation frequencies, viz., one with a maximum space step of 5 × 10^–3, decreasing to 10^–6 with a total of 621 points (mesh 5I) and the other with a maximum space step of 2 × 10^–3, with a total of 867 points (mesh 5J).With the surface boundary condition applied at x = 1.0, the l – 1 degree nonradial frequencies with CA and the l-degree frequencies without CA are in very good agreement with the frequency spacings for observed frequencies of oscillation labeled l = 1 to 5, but with the l – 1 frequencies with CA about 10 Hz or so less than the observations and the l frequencies without CA about 10 Hz or so greater than the observations. And for the Duvall and Harvey (1983) observations labeled l = 10 and l = 20, the l = 9 and l = 19 nonradial solutions with CA agree to about 5 Hz or less with the observations. Considering from the two preceeding papers in this series that increasing the density in the outer envelope and photosphere will increase the 5MB frequencies and applying the outer boundary condition at x > 1.0 will decrease the 5MB frequencies, the net affects of such changes could move one or the other set of frequencies closer to the observations — or require a slightly different model structure to obtain accurate agreements with the values of the observed frequencies throughout the 5MB.In either case, it is concluded that the first-order, radially-symmetric structure of the model outside the HZC is close to the structure of the real Sun. This is of fundamental importance because a real gas adiabatic temperature gradient (Rouse, 1964, 1971) is used in the outer convective region without free parameters.Other aspects of agreements and differences between radial and nonradial solutions, with CA and without CA are discussed. In particular, the l = 4, 6, 8, and 9 g-mode solutions with CA indicate that the observed 160.01 min period may be a common l-mode period of oscillation. More research is proposed.     

The buckling of a corrugated carbon fibre cylinder under external hydrostatic pressure

A theoretical and an experimental investigation was carried out, where a carbon fibre corrugated circular cylinder was tested to destuction under external hydrostatic pressure. The theoretical investigation was via the finite element method, where the structure was modelled with several orthotropic axisymmetric thin-walled shell elements. The experimental observations were aided with strategically placed strain gauges. Comparison between theory and experiment showed that the experimentally observed buckling pressure was a little lower than the theoretical prediction. This may have been due to the fact that the model had slight initial geometrical imperfections in the circumferenential direction.     

Plastic buckling of ring-stiffened conical shells under external hydrostatic pressure

The paper describes experimental tests carried out on three ring-stiffened cones that were tested to destruction under external hydrostatic pressure. The cones were carefully machined from EN1A Steel. All three cones failed by plastic non-symmetric bifurcation buckling in a mode commonly known as general instability. In this mode the entire ring-shell combination buckles bodily.The paper also provides a design chart using the results obtained from these three vessels, together with the results of six other vessels obtained from other tests. The design chart allows the possibility of obtaining a plastic knock down factor, so that the theoretical buckling pressures, based on elastic theory, can be divided by the plastic knockdown factor, to give the predicted buckling pressure. This method can also be used for the design of full-scale vessels.     

Dynamics of the long-period tides

The long-period tides are a tool for understanding oceanic motions at low frequencies and large scales. Here we review observations and theory of the fortnightly, monthly and pole tide constitutents. Observations have been plagued by low signal-to-noise ratios and theory by the complex lateral geometry and great sensitivity to bottom slopes. A new spectral element model is used to compute the oceanic response to tidal forcing at 2-week and monthly periods. The general response is that of a heavily damped (Q ≈ 5) system with both the energy input from the moon and the dissipation strongly localized in space. The high dissipation result is probably generally applicable to all low frequency barotropic oceanic motions. Over much of the ocean, the response has both the character of a large-scale and a superposed Rossby wave-like character, thus vindicating two apparently conflicting earlier interpretations. To the extent that free waves are excited they are consistent with their being dominated by Rossby and topographic Rossby wave components, although gravity modes are also necessarily excited to some degree. In general, a modal representation is not very helpful. The most active regions are the Southern Ocean and the western and northern North Atlantic. These results are stable to changes in geometry, topography, and tide period. On a global average basis, the dynamical response of Mm is closer to equilibrium than is Mf.     

A conceptual design of an underwater vehicle

The paper presents a conceptual design of an underwater star wars’ system, which will be more difficult to detect by the enemy than a recently proposed ‘surface’ star wars’ system.The paper suggests that for the proposed structures needed for the underwater star wars’ system, the material of construction should be a composite and not a metal, as use of the latter for large deep diving underwater vessels will result in such structures sinking to the bottom of the ocean like stones, due to the fact that they will have no reserve buoyancy. The paper also shows that composites have better sound absorption characteristics, thereby making the underwater structures difficult to detect through sonar equipment. It is proposed that these underwater structures should operate up to a depth of 7.16 miles (11.52 km), as at this depth, all of the oceans’ bottoms can be reached.The author shows that current technology can be used to construct and operate such vessels, but more progress needs to be made with metal matrix and ceramic composites, so that the hulls of underwater missiles and torpedoes can be constructed in these materials.     

Towards a political geography of United Nations peacekeeping: Some considerations

Peacekeeping missions should be viewed from various political and spatial perspectives. Firstly, there is the macro-level perspective of the UN Organization itself, particularly the respective interests of the most powerful members of the UN and permanent seat holders on the Security Council. Secondly, there are the national perspectives of the various resources and troop-contributing states to specific UN operations. Thirdly, there are the interests of the conflicting parties themselves, including governments, national armies, local militia groups, factional political leaders and local communities. An analysis of UN peacekeeping involves a complex multi-dimensional geopolitical framework that incorporates the linkages and contradictions between all these differing perspectives, from macro to micro-spatial scales. Peacekeepers themselves are not passive figures in the political and human landscapes within which they operate. Many of the activities of UN blue helmets alter landscapes and conflict scenarios. Whilst some of these changes are deliberate, such as the creation of demilitarized zones, many are unforeseen and less visible, such as the ways in which local civilian populations are affected by the presence of large numbers of foreign peacekeepers. This paper examines some of the political, social and economic consequences of peacekeeping missions in places as diverse as Cambodia, Somalia, the Lebanon and Cyprus.