The paper is focused on analysis of dynamic properties of drive system. It describes the possible ways of stability analysis and possible ways of analysis of bifurcation of steady states and possible occurrence of chaotic behavior. and Obsahuje seznam literatury
The purpose of this article is to provide an elementary introduction to the subject of chaos in the electromechanical drive systems with small MPTPRS. In this article, we explore chaotic solutions of maps and continuous time systems. These solutions are also bounded like equilibrium, periodic and quasiperiodic solutions. and POZOR! Nadpis obsahuje dvě chyby (překlepy - správně je: electromechanical (tj. vypustit chybné n) + systems (tj. vypustit druhé chybné s)
The damping or the damping forces represent certain speciality in the investigation of the internal dynamics of the transmisson systems. The special significance has this damping parameter especially in the areas of impact effects in the high-speed light aircraft and mobile transmission constructions. On the example of gear mesh in one branch of forces-flow in the presudoplanetary reducer deal the paper with some partial results of the analysis of the influence of combination damping, i.e. linear and non-linear damping, on the gear mesh dynamics.
Variational inequalities \[ U(t) \in K, (\dot{U}(t)-B_\lambda U(t) - G(\lambda ,U(t)),\ Z - U(t))\ge 0\ \text{for all} \ Z\in \ K, \text{a.a.} \ t\in [0,T) \] are studied, where $K$ is a closed convex cone in $\mathbb{R}^\kappa $, $\kappa \ge 3$, $B_\lambda $ is a $\kappa \times \kappa $ matrix, $G$ is a small perturbation, $\lambda $ a real parameter. The assumptions guaranteeing a Hopf bifurcation at some $\lambda _0$ for the corresponding equation are considered and it is proved that then, in some situations, also a bifurcation of periodic solutions to our inequality occurs at some $\lambda _I \ne \lambda _0$. Bifurcating solutions are obtained by the limiting process along branches of solutions to penalty problems starting at $\lambda _0$ constructed on the basis of the Alexander-Yorke theorem as global bifurcation branches of a certain enlarged system.
A bifurcation problem for the equation ∆u + λu − αu+ + βu− + g(λ,u)=0 in a bounded domain in N with mixed boundary conditions, given nonnegative functions α, β ∈ L∞ and a small perturbation g is considered. The existence of a global bifurcation between two given simple eigenvalues λ(1), λ(2) of the Laplacian is proved under some assumptions about the supports of the functions α, β. These assumptions are given by the character of the eigenfunctions of the Laplacian corresponding to λ(1), λ(2).