The scope of the present paper is to provide analytic solutions to the problem of the attitude evolution of a symmetric gyrostat about a fixed point in a central Newtonian force field when the potential function isV(2).We assume that the center of mass and the gyrostatic moment are on the axis of symmetry and that the initial conditions are the following: (t0)=0, (t0)=0, (t0)=(t0)=0, 1(t0)=0, 2(t0)=0 and 3(t0)=
30
.The problem is integrated when the third component of the total angular momentum is different from zero (B1 0). There now appear equilibrium solutions that did not exist in the caseB1=0, which can be determined in function of the value ofl3r
(the third component of the gyrostatic momentum).The possible types of solutions (elliptic, trigonometric, stationary) depend upon the nature of the roots of the functiong(u). The solutions for Euler angles are given in terms of functions of the timet. If we cancel the third component of the gyrostatic momentum (l3r
=0), the obtained solutions are valid for rigid bodies. 相似文献
The authors investigated the dead fragments of 22 species of submerged plants in the water from three limnological and trophical different water bodies (spring, river and pond). A total of 184 species of aquatic fungi, including 119 zoosporic and 65 conidial species were found on the fragments investigated plants. The most common fungus species were Aphanomyces laevis, Saprolegnia litoralis, Pythium rostratum (zoosporic fungi) and Acrodictys elaeidicola, Anguillospora longissima, Angulospora aquatica, Lemonniera aquatica, Mirandina corticola, Tetracladium marchalianum, Tetracladium maxiliformis, Trinacrium subtile (conidial fungi).
Most fungus species were observed on the specimens of Elodea canadensis (33 fungus species), Hippuris vulgaris f. submersa (33), Myriophyllum spicatum (34) and Potamogeton crispus (33), fewest on Ceratophyllum demersum (24), Fontinalis dalicarlica and Potamogeton nitens (each 25).
The most fungi were growing in the water from River Supraśl (107), the fewest in the water from Pond Dojlidy (99). Some aquatic fungus species were observed in the water of only one of the three water bodies – in Pond Dojlidy (30), in Spring Jaroszówka (32) and in the River Supraśl (39) species. Seventy-five species growing only on fragments of single submerged plants. A number of zoosporic and conidial species (22 and four, respectively) appeared new to Polish waters. Out of these 119 zoosporic species, some are known as parasites or necrotrophs of fish. 相似文献