The authors present a concept of constructing the equations of motion for a single-bucket pulling excavator in terms of generalised Lagrange's variables. The applied model is based on the assumption that the excavator is a system of rigid solids connected with rotational constrains of ten degrees of freedom. The essence of the proposed algorithm consists in reducing the procedure of constructing the system of excavator's motion equations to multiplication of adequate matrices. One avoids analytical or numerical derivation of the consecutive time derivatives of kinetic and potential energy of the system. The algorithm formulated in such a way may constitute a basis for constructing a numerical program for the analysis of excavator system dynamics. The proposed method of generation of Lagrange's equations can be generalised and applied to a wider class of multibody systems.

The emphasis on the territorial dimension of the public policy can be reduced to transition from a sectorial approach to an integrated territorially approach, which is based on the integration of activities of various public entities towards the territories referred not so much administratively as functionally. The functional areas (FA) is defined as spatially separated territory, which shares a common geographical differences, spatial and socio-economic conditions and the system of functional relationships and on this basis shares the uniform development objectives, ensuring effective use of its space. This understanding of the functional areas are to be the subject for intervention of the public policies. The regional development policy implemented by the voivodeship governments closely follows the findings of EU and the national strategic documents and intentionally uses a territorial approach to developmental challenges and problems. Such policy is focused (and will be focused) on the use of endogenous potential, including the territorial resources and knowledge, and will also allow for the interventions adapted to the local conditions. Thus, implementation of policy conceived in that matter is associated with geographic and thematic concentration with respect to the areas and key issues in achieving goals of the regional development. Identification of areas for which public intervention is necessary to fully exploit their endogenous potential – will be pursued with the assumption that they can have a problem character, but they can also be the potential poles of regional growth. The aim of the paper is to identify the integration processes between territorial units forming urban functional areas on regional level. In particular, it focuses on clarification the intensity of existing relationships and on the attempt to create and verify a list of criteria for delimitation of functional areas at the sub-regional level (by k-Means and Huff’s methods), assuming that each urban centre on metropolitan, national and regional level also carry-out the functions at sub-regional level.

The synsacrum is an important element of the axial skeleton in birds, both volant and flightless. Little is known about the maturation of this complex bone in penguins. In this work, the supposedly ontogenetically youngest known synsacrum of early penguins was described. The analysis of this specimen, collected within the Eocene La Meseta Formation of Seymour (Marambio) Island, Antarctic Peninsula, revealed that this bird had attained at least the fledging stage of growth. Studies of three mature synsacra recovered from the same formation focused on the synsacral canals and, using indirect reasoning, their contents. These analyses revealed that the lumbosacral intumescence of the spinal cord and its extensions, the transverse canals, had been developed roughly like those in extant penguins (and also swifts and cormorants). The neural spine extensions (a non−nervous tissue) tracing the transverse grooves of the dorsal wall of the synsacral canal are currently considered as involved in the control of walking. The presented data suggest that such a sense organ gained its current penguin configuration by the late Eocene.