Mid Sweden University

The paper concerns the general problem of a bounded final state control of non-linear dynamic systems with reference to near-optimal predictive guidance for low lift-to-drag ratio re-entry vehicles. More specifically, it addresses deriving guidance strategies capable to provide a maximal downrange maneuvrability for a maximal remaining flight time. Such robust, “guaranteed”, or assured, guidance keeps the remaining range-to-go to be coincident with the center of instant attainability domain. The paper discusses the existing guaranteed guidance strategy, and presents more general approach that provides an on-board planning of the entry trajectory, thus giving future state and control profiles. As a consequence the proposed guidance law is able to satisfy not only specified terminal conditions but also typical inequality constraints such as the maximal load factor and heat load. Computer simulations show that the algorithm can generate the feasible trajectories with equal downrange margins, using simple two-parametric families of control functions.

In this paper, it is suggested an approach and a design pattern for developing object-oriented models that need to be persistent, including the databases of moderate size, with using only the standard C++ and its file storage facilities, and without using specific C++ dialects or any support of external libraries providing the persistence. Objects of the model may be of a great variety of types, belonging to a complex class hierarchy, and are considered to be of rather general structure, containing both pointers to any other model's objects and dynamically allocated arrays of various types. The main idea consists in that all types involved are considered as classes derived from the unique base class with the minimal common interface. Classes' objects are allocated dynamically, and the pointers are kept in the model's base-class pointers container, which provides sorting, searching, and changing the objects kept. The objects' serialization, reading, and management is implemented with using the virtual functions, list of type names, and object factory technique.

This note touches a problem of developing generic mathematical software for object-oriented modeling and simulation of complex dynamic systems. More specifically, it focuses on designing the C++ class templates that could communicate with source classes comprising an object model and could process their data. This problem is of great importance for models involving a large number of different classes (types) with complex data processing. The basic idea is the use of mechanism of pointers to member functions that allows design patterns to be effectively incorporated into generic object models. In case of ODE solvers, member pointers provide access to source class member functions that describe the right-hand sides of ODEs, have control over the integration process, and make specialized computations.

The progress in development of high-precision caesium beam atomic clocks gives the opportunity for detecting the hypothetical absolute velocity of the Earth in the terrestrial experiment, using the one-way light pulses. The proposed experiment involves two non-synchronized clocks S and R to be placed at the same latitude far apart within the range of vision. A laser installed near the clock S emits short light pulses at equal time intervals during twenty-four hours, meanwhile the receiver near the clock R registers the times of pulse arrivals. The series of time intervals at the point R will display diurnal variations, which can be used for calculating the equatorial component of absolute velocity of the Earth.

The paper focuses on the problem of developing an electrodynamic model of the supercurrent-growing transition stage in the Meissner effect. The London theory giving the quantum-mechanical explanation for the steady superconducting state says nothing about the forces that evoke the electric current in the transition stage. The classical electrodynamics is also inapplicable in the transition stage through the zero forces predicted by Faradey's law. This gap caused the author to look deeply inside the fundamentals of the classical electrodynamics. The analysis is focused on the basic problem of calculating the force on a stationary point charge from a uniformly moving point charge and reveals two arguable assumptions in the classic theory. The first is the extension of Coulomb's law for calculating the force exerted by a stationary charge on a uniformly moving charge. This assumption is in contradiction with the retarded action principle and overlooks the existence of the longitudinal force that might be responsible, in particular, for the Meissner effect and for maintaining the stability of Rutherford's atom. The second assumption about the point-like charges makes the classic formula for Lorentz force physically unsound at normal temperatures when we deal with fermions rather than point charges with zero spin. Therefore a more complex model of the electron should be used, something like a spinning charged ring. One can safely regard free electrons as point charges only for superconductors due to the formation of Cooper pairs. The above considerations have formed the basis of the computing model describing the transition stage in the Meissner effect and explaining the absence of electric current in the system comprising "normal conductor - permanent magnet"