The main problem of artificial satellite theory for small and moderate eccentricities

Perturbation techniques based on Lie transforms as suggested by Deprit were used as the theoretical foundation for programming the analytical solution of the Main Problem in Satellite Theory (all gravitational harmonics being zero exceptJ ₂). The collection of formulas necessary and sufficient to construct an ephemeris is given in the exposition. Short and long period displacements, as well as the secular terms, have been obtained up to the third order inJ ₂ as power series of the eccentricity. They result from two successive completely canonical transformations which it has been found convenient not to compose into a unique transformation. Division by the eccentricity appears nowhere in the developments-neither explicitly nor implicitly. The determination of the constants of motion from the initial conditions has been given an elementary solution that is both complete and explicit without being iterative. The program was developed by Rom from MAO's package of subroutines forMechanizedAlgebraicOperations. Reliability tests have been run in two instances: in-track errors for ANNA 1B are only 20 cm after 210 days in orbit, while for RELAY II, they are 2.4 m, even after 350 days in orbit.     

An Excel Macro to Plot the HFE‐Diagram to Identify Sea Water Intrusion Phases

A hydrochemical facies evolution diagram (HFE‐D) is a multirectangular diagram, which is a useful tool in the interpretation of sea water intrusion processes. This method note describes a simple method for generating an HFE‐D plot using the spreadsheet software package, Microsoft Excel. The code was applied to groundwater from the alluvial coastal plain of Grosseto (Tuscany, Italy), which is characterized by a complex salinization process in which sea water mixes with sulfate or bicarbonate recharge water.     

A methodology for the probabilistic assessment of behaviour factors

Given the importance that traditional force-based seismic design still currently exhibits, studies addressing issues related to the definition of the behaviour factor values are considered to be of most interest. A probabilistic methodology is proposed for the calibration of the q-factor relating its value with two fundamental parameters, the displacement ductility capacity measured at a relevant location of the structure and the failure probability P _f . The general foundation of this procedure is based on the probabilistic quantification of the seismic action and, by applying a transformation procedure, of the structural seismic demand in terms of displacement ductility. By recalling well established structural reliability procedures and by making use of nonlinear analysis methods, both static and dynamic, a general probabilistic framework, which is able to relate the ductility capacity, the failure probability P _f and the behaviour factor, is defined. In order to illustrate some of the potentialities of the methodology, an application example is presented, addressing the q-factor assessment for a set of regular and irregular reinforced concrete frame structures, enforcing a given P _f and two different ductility levels.