We study sub-Riemannian structures obtained by the restriction of the standard left-invariant Riemannian metric to a right-invariant completely nonholonomic distribution on the second Heisenberg group. The corresponding Hamiltonian system is completely integrable and we study its solutions in this paper. We obtain a complete classification of the geodesic curves by studying the reduced Hamiltonian system. Moreover, we compute r(t) as the first step of the quadrature in the reduced system in the hyperspherical coordinates and present numerical examples that illustrate the theoretical results.
This paper investigates the stochastic stability of gyroscopic viscoelastic systems subjected to parametric wide-band noise excitation. The analysis focuses on both moment stability, using moment Lyapunov exponents, and almost-sure stability, via the largest Lyapunov exponent. The wide-band noises considered include Gaussian white noise and Ornstein–Uhlenbeck noise. The Stratonovich stochastic differential equations governing the system with small damping and weak excitation are first converted to Itô stochastic differential equations through stochastic averaging techniques. An elegant mathematical framework is then introduced to approximate the moment Lyapunov exponents through stochastic transformations and an eigenvalue problem. The largest Lyapunov exponent is subsequently derived based on its relationship with the moment Lyapunov exponents. An application example involves deriving the stochastic equations of motion for an axially moving band system with fluctuating tension, analyzing its stochastic stability. The analytical approximations are validated via Monte Carlo simulations and compared with results from the literature. The study also discusses the influence of various parameters on the system’s stability, with potential applications in engineering fields.
This research builds upon Çelik’s earlier study [1], which explored various flow patterns and constructed a bifurcation diagram for the flow with Stokes approximation in a Z-shaped domain driven by dual lids. In this study, enhanced solutions near the re-entrant corner are initially derived using the asymptotic matching technique. These solutions direct attention towards a comprehensive analysis of flow structures and behaviors at the re-entrant corner point. The formation and bifurcation of the separation bubble that appears near the corner is investigated in detail. Subsequently, the (h1, h2) control space diagram, which was previously developed on the basis of cavity height parameters, is recreated for a Reynolds number of 50. Additionally, the impact of the Reynolds number (Re) on vortex formation is analyzed. The findings indicate that at Re = 50, distinct flow patterns occur, and an increase in the Reynolds number accelerates vortex formation, leading to earlier transitions in flow topology and more complex bifurcation scenarios.
From the three-dimensional linear theory of elasticity, two- and one-dimensional descriptions are derived by involving the consistent-approximation approach. The pseudo-reduction technique yields well-known and higher-order theories for quasi two-dimensional and quasi one-dimensional structural members.
In formula (1.1) of the quoted article, the expression of the excenticity eH of ellipses in the Hooke’s problem is wrong. It must be replaced with the following one eH = √2σ/1+σ, where σ = √1−KL2/mE2. The reader is kindly asked to forgive this error which, however, in no way affects the content of the article. Link to the corrected article 10.2298/TAM220213005C
