A steering control system for the tractor – semi-trailer combination vehicle with the electromechanical transmission

The article offers an algorithm for the operation of the steering and active drive control system of a saddle-type tractor – trailer combination. The algorithm allows reducing the width of the cornering corridor when maneuvering at low speeds. In the combination vehicle under study, all the wheels of the tractor and semi-trailer are driving and steered. The algorithm of the steering control system takes into account the current values of the folding angle and speed of the combination vehicle. The active drive control is based on the analysis of the forces in the coupling device. The efficiency and effectiveness of the proposed algorithm has been proved using computational experiments.

Analysis of a mass-spring-relay system with periodic forcing

The dynamics of a hysteretic relay oscillator with harmonic forcing is investigated. Periodic excitation of the system results in periodic, quasi-periodic, chaotic and unbounded behavior. An explicit Poincaré map is constructed with an implicit constraint on the switching time. The stability of the fixed points of the Poincaré map corresponding to period-one solutions is investigated. By varying the forcing parameters, we observed a saddle-center and a pitchfork bifurcation of two centers and a saddle-type fixed point. The global dynamics of the system exhibits discontinuity induced bifurcations of the fixed points.

Improving the performance of a ploughing tractor by means of an auxiliary carriage with motorized axle

The article describes the analysis of results from field tests on ploughing units based on a modular draft device (MDD). This device is named MDD-100 and consists of an energy module and a technological module. The energy module is a universal tractor with a rated draft resistance of 16 kN. The technological module is an additional axle, equipped with an active wheel drive, a threepoint hitch linkage, and a saddle-type semi-trailer. During the working process, the draft resistance of the energy and the technological modules of the MDD-100 add up. As a result, the draft resistance of the latter may reach 26 kN, and more. This allows the MDD-100 to be classified as a draft device in traction class 3 and be used with agricultural machines with a large working width. The MDD-100 was tested with a five-bottom mounted plough with a working width of 1.75 m and a draft resistance of 24-28 kN. The best option for driving the MDD-100 with a plough was its movement with the right-side wheels in the furrow. The draft resistance of the plough would decrease by 12.0%, if the option of the MDD-100 outside the furrow is used. This ensured a 12.8% reduction in the skidding of the MDD-100 wheels and a 13.1% decrease of fuel consumption for the ploughing unit. Compared to a 4WD tractor, the use of a modular draft device with a 6WD wheel arrangement offered a greater stability of the ploughing depth.

Analysis of a Mass-Spring-Relay System With Periodic Forcing

The dynamics of a hysteretic relay oscillator with harmonic forcing is investigated. Periodic excitation of the system results in periodic, quasi-periodic, chaotic and unbounded behavior. A Poincare map is constructed to simplify the mathematical analysis. The stability of the xed points of the Poincare map corresponding to period-one solutions is investigated. By varying the forcing parameters, we observed a saddle-center and a pitchfork bifurcation of two centers and a saddle type xed point. The global dynamics of the system is investigated, showing discontinuity induced bifurcations of the xed points.

Radiatively-driven black-hole winds revisited

We examine general relativistic radiatively-driven spherical winds, using the basic equations for relativistic radiation hydrodynamics under the moment formalism. Moment equations are often closed, using the equilibrium diffusion approximation, which has an acausal problem, and furthermore, gives nodal-type critical points. Instead, we use the nonequilibrium diffusion approximation with a closure relation of a variable Eddington factor, f(τ, β), where τ is the optical depth and β is the flow speed normalized by the speed of light. We then analyse the critical properties in detail for several parameters, and found that there appear saddle-type critical points as well as nodal type and spiral one. The most suitable type is the saddle one, which appears in a region close to a black hole. We also calculate transonic solutions with typical parameters, and show that the luminosity is almost comparable to the Eddington luminosity, the gas is quickly accelerated in the vicinity of the black hole, and wind terminal speeds are on the order of 0.1–0.3 c. These results of radiatively-driven black hole winds can be applied, e.g. to ultra-fast outflows (UFOs), which are supposed to be fast outflows from the vicinity of super massive black holes.

Zero–Hopf Bifurcations in Three-Dimensional Chaotic Systems with One Stable Equilibrium

In [Molaie et al., 2013] the authors provided the expressions of 23 quadratic differential systems in [Formula: see text] with the unusual feature of having chaotic dynamics coexisting with one stable equilibrium point. In this paper, we consider 23 classes of quadratic differential systems in [Formula: see text] depending on a real parameter [Formula: see text], which, for [Formula: see text], coincide with the differential systems given by [Molaie et al., 2013]. We study the dynamics and bifurcations of these classes of differential systems by varying the parameter value [Formula: see text]. We prove that, for [Formula: see text], all the 23 considered systems have a nonisolated zero–Hopf equilibrium point located at the origin. By using the averaging theory of first order, we prove that a zero–Hopf bifurcation takes place at this point for [Formula: see text], which leads to the creation of three periodic orbits bifurcating from it for [Formula: see text] small enough: an unstable one and a pair of saddle type periodic orbits, that is, periodic orbits with a stable and an unstable manifold. Furthermore, we numerically show that the hidden chaotic attractors which exist for these systems when [Formula: see text] are obtained by period-doubling route to chaos.