Point-connected rigid bodies in a topological tree

Identical equations of motion are shown to emerge for a system ofn+1 rigid bodies all interconnected byn points, each of which is common to two bodies, by means of each of the following derivation procedures, all of which employ a kinematical identity developed by Hooker and Margulies: The Hooker-Margulies/Hooker equations; Kane's quasicoordinate formulation of D'Alembert's principle; the combination of Lagrange's generalized coordinate equations and Lagrange's quasicoordinate equations; and the combination of Lagrange's generalized coordinate equations and the vector rotational equationM=H applied to the total system and resolved into a vector basis fixed in a reference body of the system. Thus the previously published Hooker-Margulies/Hooker equations are shown to be the natural result of several derivation procedures other than the Newton-Euler method originally used, provided that the central kinematical identity of the original derivation of Hooker and Margulies is employed.     

Palaeosecular variation over the past 5 Myr based on a new generalized database

A generalized database of global palaeomagnetic data from 3719 lava flows and thin dykes of age 0–5 Ma has been constructed for use with a relational database management system. The database includes all data whose virtual geomagnetic poles (VGP) lie within 45 of the spin axis and can be used for studies of palaeosecular variation and for geomagnetic field modelling. Because many of these data were collected and processed more than 15–20 years ago, each result has been characterized according to the demagnetization procedures carried out. Analysis of these data in terms of the latitude variation of the angular dispersion of VGPs (palaeosecular variation from lavas) strongly suggests that careful data selection is required and that many of the older studies may need to be redone using more modern methods. Differences between the angular dispersions for separate normal- and reverse-polarity data sets confirm that many older studies have not been adequately cleaned magnetically. Therefore, the use of the database for geomagnetic field modelling should be carried out with some caution. Using a VGP cut-off angle that varies with latitude, the best data set consists of 2636 results that show a smooth increase of VGP angular dispersion with latitude. Model G for palaeosecular variation, which is based on modelling of the antisymmetric (dipole) and symmetric (quadrupole) dynamo families, provides a good fit to these results.     

Mineral inclusions in diamonds from the Sputnik kimberlite pipe, Yakutia

The Sputnik kimberlite pipe is a small “satellite” of the larger Mir pipe in central Yakutia (Sakha), Russia. Study of 38 large diamonds (0.7-4.9 carats) showed that nine contain inclusions of the eclogitic paragenesis, while the remainder contain inclusions of the peridotitic paragenesis, or of uncertain paragenesis. The peridotitic inclusion suite comprises olivine, enstatite, Cr-diopside, chromite, Cr-pyrope garnet (both lherzolitic and harzburgitic), ilmenite, Ni-rich sulfide and a Ti-Cr-Fe-Mg-Sr-K phase of the lindsleyite-mathiasite (LIMA) series. The eclogitic inclusion suite comprises omphacite, garnet, Ni-poor sulfide, phlogopite and rutile. Peridotitic ilmenite inclusions have high Mg, Cr and Ni contents and high Nb/Zr ratios; they may be related to metasomatic ilmenites known from peridotite xenoliths in kimberlite. Eclogitic phlogopite is intergrown with omphacite, coexists with garnet, and has an unusually high TiO₂ content. Comparison with inclusions in diamonds from Mir shows general similarities, but differences in details of trace-element patterns. Large compositional variations among inclusions of one phase (olivine, garnet, chromite) within single diamonds indicate that the chemical environment of diamond crystallisation changed rapidly relative to diamond growth rates in many cases. P-T conditions of formation were calculated from multiphase inclusions and from trace element geothermobarometry of single inclusions. The geotherm at the time of diamond formation was near a 35 mW/m² conductive model; that is indistinguishable from the Paleozoic geotherm derived by studies of xenoliths and concentrate minerals from Mir. A range of Ni temperatures between garnet inclusions in single diamonds from both Mir and Sputnik suggests that many of the diamonds grew during thermal events affecting a relatively narrow depth range of the lithosphere, within the diamond stability field. The minor differences between inclusions in Mir and Sputnik may reflect lateral heterogeneity in the upper mantle.