A contribution to the theory of the extended Lagrangian formalism for rheonomic systems

In this paper the generalization of the notion of variation in the extended Lagrangian formalism for the rheonomic mechanical systems (Đ. Mušicki, 2004) is formulated and analyzed in details. This formalism is based on the extension of a set of generalized coordinates by new quantities, which determine the position of the frame of reference to which the chosen generalized coordinates refer. In the process of varying, the notion of variation is extended so that these introduced quantities, being additional generalized coordinates, must also to be varied, since the position of each particle of this system is completely determined only by all these generalized coordinates. With the consistent utilization of this notion of variation, the main results of this extended Lagrangian formalism are systematically presented, with the emphasis on the corresponding energy laws, first examined by V. Vujičić (1987), where there are two types of the energy change laws dE/dt and the corresponding conservation laws. Furthermore, the generalized Noether's theorem for the nonconservative systems with the associated Killing's equations (B. Vujanović, 1978) is extended to this formulation of mechanics, and applied for obtaining the corresponding energy laws. It is demonstrated that these energy laws, which are more general and more natural than the usual ones, are in full accordance with the corresponding ones in the vector formulation of mechanics, if they are expressed in terms of quantities introduced in this extended Lagrangian formalism. Finally, the obtained results are illustrated by an example: the motion of a damped linear harmonious oscillator on an inclined plane, which moves along a horizontal axis, where it is demonstrated that there is valid an energy-like conservation law of Vujanović's type

Tracking and Estimation of Multiple Cross-Over Targets in Clutter

Tracking problems, including unknown number of targets, target trajectories behaviour and uncertain motion of targets in the surveillance region, are challenging issues. It is also difficult to estimate cross-over targets in heavy clutter density environment. In addition, tracking algorithms including smoothers which use measurements from upcoming scans to estimate the targets are often unsuccessful in tracking due to low detection probabilities. For efficient and better tracking performance, the smoother must rely on backward tracking to fetch measurement from future scans to estimate forward track in the current time. This novel idea is utilized in the joint integrated track splitting (JITS) filter to develop a new fixed-interval smoothing JITS (FIsJITS) algorithm for tracking multiple cross-over targets. The FIsJITS initializes tracks employing JITS in two-way directions: Forward-time moving JITS (fJITS) and backward-time moving JITS (bJITS). The fJITS acquires the bJITS predictions when they arrive from future scans to the current scan for smoothing. As a result, the smoothing multi-target data association probabilities are obtained for computing the fJITS and smoothing output estimates. This significantly improves estimation accuracy for multiple cross-over targets in heavy clutter. To verify this, numerical assessments of the FIsJITS are tested and compared with existing algorithms using simulations

Theory of interacting electrons on the honeycomb lattice

The low-energy theory of electrons interacting via repulsive short-range interactions on graphene's honeycomb lattice at half filling is presented. The exact symmetry of the Lagrangian with local quartic terms for the Dirac field dictated by the lattice is D_2 x U_c(1) x (time reversal), where D_2 is the dihedral group, and U_c(1) is a subgroup of the SU_c(2) "chiral" group of the non-interacting Lagrangian, that represents translations in Dirac language. The Lagrangian describing spinless particles respecting this symmetry is parameterized by six independent coupling constants. We show how first imposing the rotational, then Lorentz, and finally chiral symmetry to the quartic terms, in conjunction with the Fierz transformations, eventually reduces the set of couplings to just two, in the "maximally symmetric" local interacting theory. We identify the two critical points in such a Lorentz and chirally symmetric theory as describing metal-insulator transitions into the states with either time-reversal or chiral symmetry being broken. In the site-localized limit of the interacting Hamiltonian the low-energy theory describes the continuous transitions into the insulator with either a finite Haldane's (circulating currents) or Semenoff's (staggered density) masses, both in the universality class of the Gross-Neveu model. The picture of the metal-insulator transition on a honeycomb lattice emerges at which the residue of the quasiparticle pole at the metallic and the mass-gap in the insulating phase both vanish continuously as the critical point is approached. We argue that the Fermi velocity is non-critical as a consequence of the dynamical exponent being fixed to unity by the emergent Lorentz invariance. Effects of long-range interaction and the critical behavior of specific heat and conductivity are discussed.Comment: 16 revtex pages, 4 figures; typos corrected, new and updated references; published versio

Predicting of lead distribution and immobilization in soil of the region of lignite mining (Rudovci, Serbia)

Lead distribution and immobilization in cultivated soils in Rudovci, Serbia was investigated. Sampling was carried out by the method recommended by ICP-Forests Manual, 2006, Part III Sampling and analysis of Soil. The sampling geometry was systematically designed with a random component. The maximum sampling depth was 100 cm and lead distribution was monitored during 425 days. First sample was taken after 50 days and every single next sample was taken after 50 days except for the last sample which was taken after 25 days. Before the profile contamination, physical and chemical soil analysis has been done. The cation exchange capacity of the soil was done because media affect mobility cations (anions) in soil. The effect of immobilizations of Pb is highest in the second horizons where the depth of investigating soil is 25-50 cm

Predicting of lead distribution and immobilization in soil of the region of lignite mining (Rudovci, Serbia)

Lead distribution and immobilization in cultivated soils in Rudovci, Serbia was investigated. Sampling was carried out by the method recommended by ICP-Forests Manual, 2006, Part III Sampling and analysis of Soil. The sampling geometry was systematically designed with a random component. The maximum sampling depth was 100 cm and lead distribution was monitored during 425 days. First sample was taken after 50 days and every single next sample was taken after 50 days except for the last sample which was taken after 25 days. Before the profile contamination, physical and chemical soil analysis has been done. The cation exchange capacity of the soil was done because media affect mobility cations (anions) in soil. The effect of immobilizations of Pb is highest in the second horizons where the depth of investigating soil is 25-50 cm

Noether’s theorem for nonconservative systems in quasicoordinates

In this paper the generalized Noether’s theorem is given in quasicoordinates for the systems of particles, the motion of which can be presented in quasicoordinats and quasivelocities. After a systematic review of the calculus with quasicoordinates and the corresponding Boltzmann-Hamel’s equations of motion, the total variation of action is given in quasicoordinates. Then, the corresponding generalized Noether’s theorem is formulated, valid for nonconservative systems as well, which is obtained from the total variation of action and corresponding Boltzmann-Hamel’s equations. So formulated Noether’s theoerm in quasicoordinates is valid for all conservative and nonconservative systems without any limitation. It is applied to obtain the corresponding energy integrals in quasicoordinates for conservative and nonconservative systems, in the latter case these are energy integrals in broader sense. The obtained results are illustrated by a characteristic example, where the corresponding energy integral is found. This generalized Neother’s theorem is equivalent, but not in the form and with some limitation, to the corresponding Noether’s theorem formulated by Dj. Djuki.c [13], which is obtained from the invariance of total variation only of element of action Δ(). However, for nonconservative systems the Lagrangian , appearing in this relations, represents not the usual, but an equivalent Lagrangian, which completely determines the considered system, including the influence of nonpotential forces. Therefore, the cited Noether’s theorem is valid only for these nonconservative systems for which it is possible to find such equivalent Lagrangian, (what for the natural systems is mostly possible)