Investigation of influence of high-frequency vibrations on the stability of stationary rotations of Lagrange’s top

The motion of Lagrange’s top in the homogeneous gravity field is considered under the assumption that its suspension point accomplishes a specified high-frequency periodic motion with small amplitude (fast vibrations) in the three-dimensional space. The investigation is carried out in the framework of the approximate autonomous system of canonical equations of motion. Stationary rotations of Lagrange’s top around its dynamical symmetry axis for a number of particular cases of the suspension point motions are found as positions of equilibriums of the reduced two-degree-of-freedom system. The linear and nonlinear analysis for their stability is carried out. The problems discussed in the report are new and have no analogues in domestic and foreign literature

Quasistatic approach in problems of the viscoelastic body dynamics in gravitation field

The sum of the number of second order polynomial value representations by the sum of two numbers squared is considered in the paper with the aim of the asymptotical formula obtaining for sum of 31 greater than or equal to z greater than or equal to T1r(f(z)). As a result an asymptotical formula with one main member for the sum of the number of quadratic polynomial representations by the sum of two numbers squared in the general case has been obtained as well as an asymptotical formula with two members before remainder for sum of 31 greater than or equal to z greater than or equal to T=1r(az221+bz+c)Available from VNTIC / VNTIC - Scientific & Technical Information Centre of RussiaSIGLERURussian Federatio