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EN
The purpose of this study was to reconstruct the early phase of scientific research conducted at the Department of Biomechanics of the College of Physical Education and since 1972 at the University School of Physical Education in Poznań, with special attention paid to the works on biomechanics of rowing, carried out as part of the Ministerial Project PR 105 entitled The effectiveness of training, sports competition as well as regeneration in sports. Two kinds of biomechanical research are described: the several years’ expert research conducted on the Rowing National Team in an original two-module Rowing Pool Testing Station BTW-1, as well as research on geometric optimization of the rowing station, conducted under real conditions, in reservoirs, with the use of a prototypical, unique at that time, computer measurement system BIOMIK, installed in the rower’s own boat. The projects were carried out by doctoral students from the Department of Biomechanics and the Department of Clinical Biomechanics, Andrzej Lisiecki and Wojciech Mikołajczyk, respectively.
EN
The purpose of this study is to reconstruct the early phase of scientific research conducted at the Department of Biomechanics of the University School of Physical Education in Poznań, particularly the work on biomechanics of rowing, conducted as part of the Ministerial Project PR 105, entitled “The effectiveness of training and competition as well as regeneration in sports”. Three kinds of research have been described, carried out with the use of the rowing ergometers. The first was the research on neuromuscular coordination in the rowing cycle, the second was the research on kinematic and dynamic characteristics of rowing on the Universal Rowing Ergometer UEW-1, while the last one concerned determination of maximum forces generated by functional muscle groups in two characteristic rowing positions within the closed biochain of the torso and the limbs.
PL
Celem pracy jest pokazanie, że pewne wyniki dotyczące minimalizacji pracy potrzebnej do pokonania oporów ruchu mogą być otrzymane w prosty sposób z równania Eulera-Lagrange'a - warunku koniecznego ekstremum funkcjonału. Równanie to jest na ogół równaniem różniczkowym drugiego rzędu. W przypadku gdy funkcja podcałkowa minimalizowanego funkcjonału liniowo zależy od pochodnej, równanie to degeneruje się do pewnego równania algebraicznego. Krzywa reprezentująca rozwiązanie tego równania nosi nazwę łuku osobliwego. W pracy zostaną przedstawione dwa przypadki minimalizacji pracy potrzebnej do pokonania oporów ruchu: w kolarstwie i wioślarstwie.
EN
It has been shown in the paper, that some results referring to minimization of the work necessary to overcome the resistance of motion may be obtained in the simple way using Euler-Lagrange's equation. In general, this equation is an ordinary differential equation of the second order. If the function in the functional is linear with respect to the derivative it degenerates to an algebraic equation. The curve that represents the solution of this equation is called the singular arc. Two minimization problems of the work necessary to overcome the resistive forces have been considered in cycling and rowing.
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