In this paper, optimal distributions of loads on the three supports of the body are obtained. These loads provide the corresponding maximum external vertical moment of active forces required for the static equilibrium of the body under dry friction conditions. This moment is obtained in explicit form for various situations. It is shown that, if this threshold moment is exceeded even slightly (in the nondegenerate situation where the body moves with all three points in contact with the plane), the body begins to rotate about the vertical axis passing through the center of the circle circumscribed around the supporting triangle. Furthermore, it is shown that the resulting maximum moment of active forces about the axis does not depend on the horizontal projection of the principal vector of the active forces. Degenerate situations where the body moves with only two points in contact with the plane are also discussed.
After publication of the original article [1], the authors identified inaccuracies in the derivation of the equations of motion of a spherical robot. The corrections provided in this erratum do not affect the design of the stabilizing regulator and the conduct of experimental studies.
The electroplasticity effect involves reduced yield stress in deformed metals under pulsed electric currents, unexplained by Joule heating alone. In coarse-grained metals, plastic deformation primarily occurs via dislocation slip, modeled here using Frenkel – Kontorova kinks. This numerical study explores how electric pulses affect dislocation mobility, comparing two mechanisms: Joule heating localized at dislocations and electron wind transferring momentum. Key findings show that, at lower temperatures, Joule heating enhances dislocation mobility more significantly, while higher temperatures favor electron wind dominance. Within an intermediate temperature
This paper considers the iterative learning control design problem for discrete-time systems with uncertain parameters and input saturation. To accelerate convergence of the learning process, a combination of heavy-ball methods from optimization theory and the Lyapunov vector function method for repetitive processes is proposed. An example is given, including a comparison with known results.
The complementary subspaces (CS) method is aimed at numerically solving equations of the form $P_{\cal U}(Av-f)=0$ emerging when evolutionary equations are integrated by spectral methods. Here $v$ must belong to the finite-dimensional space ${\cal V}$ comprised of functions satisfying the prescribed boundary conditions and $P_{\cal U}$ is an orthogonal projection on a finite-dimensional space ${\cal U}$. The idea of the CS method is to find the solution to the original problem by solving a modified problem, $P_{\cal G}(Aw-\widetilde{f})=0$, $w\in{\cal W}$, and either adding the correction $\widetilde{f}-f$ before solving the modified problem, or computing the correction $v-w$ afterwards. The spaces ${\cal W}$ and ${\cal G}$ are chosen in such a way that solving the modified problem requires less operations than the original one. The method was introduced in [23]; we propose now its modification allowing more freedom in choosing the spaces for the modified problem and in computing the correction. The algorithm is discussed in the general form and in the case of the spaces spanned by linear combinations of Chebyshev polynomials. The method is applied for numerical investigation of convective flows in a plane horizontal layer heated from below and rotating about an inclined axis with no-slip horizontal boundaries. For the employed values of control parameters the temporal behavior is comprised of repeating events and is possibly related to heteroclinic connections between unstable steady states.
