analytical solution

Solution of the equation of force of impact of solids expressed by the Ateb-sine

A nonlinear differential equation of the force of direct central quasistatic impact of elastic bodies bounded in the area of their contact by rotation surfaces is compiled. To determine the coefficients of the equation and the order of its degree nonlinear force, we used the well-known solution of the axisymmetric contact problem of elasticity theory, constructed in due time by I. Ya. Shtaerman, for the case of dense static contact of bodies, when the order of their boundary surfaces is not lower than the second.

On Free Oscillations of a Quadratic Nonlinear Oscillator

A free oscillations of a system with one degree of freedom, caused either by the initial deviation from the stable equilibrium position or by the initial velocity provided by the oscillator in this position was considered. Analytical solutions of the nonlinear Cauchy problem for a second-order differential equation were constructed. The solutions are expressed in terms of Jacobi's periodic elliptic functions relating to occultation of special functions.