Vol. 10, No. 4
Vol. 10, No. 4, 2014
Kuznetsov A. P., Migunova N. A., Sataev I. R., Sedova Y. V., Turukina L. V.
Abstract
Ensembles of several chaotic R¨ossler oscillators are considered. It is shown that a typical phenomenon for such systems is the emergence of invariant tori of different and sufficiently high dimension. The possibility of a quasiperiodic Hopf bifurcation and of the cascade of such bifurcations based on tori of increasing dimension is demonstrated. The domains of resonant tori are revealed whose boundaries correspond to a saddlenode bifurcation. Within areas of resonant modes the torusdoubling bifurcations and tori destruction are observed.

Kulakov M. P., Neverova G. P., Frisman E. Y.
Abstract
This article researches model of two coupled an age structured populations. The model consists of two identical twodimensional maps demonstrating the Neimark – Sacker and perioddoubling bifurcations. The “bistability” of dynamic modes is found which is expressed in a coexistence the nontrivial fixed point and periodic points (stable 3cycle). The mechanism of loss stability and formation of complex hierarchy for multistable states are investigated.

Grines V. Z., Gurevich E. Y., Zhuzhoma E. V., Zinina S. K.
Abstract
We obtain properties of threedimensional phase space and dynamics of Morse–Smale diffeomorphism that led to existence of at least one heteroclinical curve in nonwandering set of the diffeomorphism. We apply this result to solve a problem of existence of separators in magnetic field of plasma.

Kozlov V. V.
Abstract
This paper is concerned with the problem of first integrals of the equations of geodesics on twodimensional surfaces that are rational in the velocities (or momenta). The existence of nontrivial rational integrals with given values of the degrees of the numerator and the denominator is proved using the Cauchy–Kovalevskaya theorem.

Markeev A. P.
Abstract
We consider the canonical differential equations describing the motion of a system with one degree of freedom. The origin of the phase space is assumed to be an equilibrium position of the system. It is supposed that in a sufficiently small neighborhood of the equilibrium Hamiltonian function can be represented by a convergent series. This series does not include terms of the second degree, and the terms of the third and fourth degrees are independent of time. Linear real canonical transformations leading the terms of the third and fourth degrees to the simplest forms are found. Classification of the systems in question being obtained on the basis of these forms is used in the discussion of the stability of the equilibrium position.

Polekhin I. Y.
Abstract
Two examples concerning application of topology in study of dynamics of inverted plain mathematical pendulum with pivot point moving along horizontal straight line are considered. The first example is an application of the Wazewski principle to the problem of existence of solution without falling. The second example is a proof of existence of periodic solution in the same system when law of motion is periodic as well. Moreover, in the second case it is also shown that along obtained periodic solution pendulum never becomes horizontal (falls).

Kilin A. A., Bobykin A. D.
Abstract
The problem of motion of a vehicle in the form of a platform with an arbitrary number of Mecanum wheels fastened on it is considered. The controllability of this vehicle is discussed within the framework of the nonholonomic rolling model. An explicit algorithm is presented for calculating the control torques of the motors required to follow an arbitrary trajectory. Examples of controls for executing the simplest maneuvers are given.

Borisov A. V., Erdakova N. N., Ivanova T. B., Mamaev I. S.
Abstract
In this paper we investigate the dynamics of a body with a flat base sliding on a inclined plane under the assumption of linear pressure distribution of the body on the plane as the simplest dynamically consistent friction model. Computeraided analysis of the system’s dynamics on the inclined plane using phase portraits has allowed us to reveal dynamical effects that have not been found earlier.

Kilin A. A., Karavaev Y. L.
Abstract
The kinematic control model for a spherical robot with an internal omniwheel platform is presented. We consider singularities of control of spherical robot with an unbalanced internal omniwheel platform. The general algorithm of control of spherical robot according to the kinematical quasistatic model and controls for simple trajectories (a straight line and in a circle) are presented. Experimental investigations have been carried out for all introduced control algorithms.

Rust . C., Asada H. H.
Abstract
A Remotely Operated Vehicle (ROV) is developed for use in the inspection of underwater structures in hazardous environments. The vehicle presented can change orientation like an eyeball using a novel gimbal mechanism for moving an internal eccentric mass. Combined with a pair of thrusters, the Eyeball ROV can move in any direction with nonholonomic constraints. In this paper the design concept is presented first, followed by dynamic and hydrodynamic analysis. Due to poor open loop stability characteristics, stability a ugmentation is implemented using onboard sensors and was de signed and tested in simulation. A physical proofofconcept prototype is also presented.
