**Journal of Theoretical and Applied Mechanics**

Volume 32, Number 3, 2002

**Contents**

**P. Vassileva, D. Petrova, H. Hristov, A. Cheremensky**

Institute of Mechanics, Bulgarian Academy of Sciences,

Acad. G. Bonchev Str., Bl. 4, 1113 Sofia, Bulgaria,

*e-mail: *ana@bgcict.acad.bg*
*

**Control Design in One Non-orthogonal Attitude Problem**

Abstract. This paper gives control design in the case where a body "must point toward Earth, while another part (a solar panel) must face the sun" [8], i.e., one vector is immobile with respect to the Earth-centered-inertial frame, but an other one is rotating with time-constant angular velocity.

Key Words: attitude control, Lyapunov functions, system theory, feedback control, non-linear control.

**V. Petrov, N. Georgiev **

Institute of Mechanics, Bulgarian Academy of Sciences,

Acad. G. Bonchev Str., Bl.4, 1113 Sofia, Bulgaria,

*e-mail: *valko@imbm.bas.bg* *

**J. Kurths**

Institute of Physics, Potsdam University,

D-14415, Germany,

*e-mail: *juergen@agnld.uni-potsdam.de*
*

**Determining Phase Space Dimension of a Dynamical System from Analytic
Time Series**

Abstract. In this paper we propose an analytic consideration of the problem for determining the dimension of phase space of dynamical system from a time series. More in detail, the consideration is made under condition that an analytic function is given by a formula or as a solution of some dynamical system (differential equation}. In both cases (formula and solution), the analytic function is treated as a continuos time series. Two theorems for existence, uniqueness and order determination of a dynamical system in the form of an ordinary differential equation are formulated and proved. For this purpose, two cases of time series originated from first and arbitrary order of dynamical systems are considered.

Key words:** **reconstruction, differential equation, simple curve,
regular curve, embedding.

**St. Bachvarov, S. Delcheva**

Engineering Pedagogical Faculty-Sliven, Technical University–Sofia,

59, Bourgasko shosse Str., 8800 Sliven, Bulgaria

**V. Zlatanov**

Higher Institute of Food and Flavour Industry,

26, Maritza Str., 4000 Plovdiv, Bulgaria,

*e-mail: vassil60@Hotmail.com*

DYNAMICS OF MACHINE AGGREGATES WITH IDEALLY RIGID LINKS AND FRICTION COUPLING BETWEEN THE POWER MACHINE AND THE GEARING (Part I)

Abstract. The paper treats the dynamics of machine aggregate set in motion by an asynchronous electric motor and a working machine with constant, linear and quadratic characteristics of the resistance forces. A number of devices are mounted between the motor and the working machine: a switching friction coupling, a reducer with constant gear ratio, permanently switched on coupling, and ŕ ideally rigid shaft. Motion of the latter is reduced to the electric motor shaft. Transition processes of acceleration, stopping and the loading of the aggregate shaft-conductor are also studied. The results found are illustrated by means of a numerical example, which considers an aggregate with real parameters.

Key words: machine aggregate, reducer (gearing), friction coupling, transitory processes under acceleration and stopping, dynamic loads.

**P. Atten **

LEMD, CNRS & Joseph Fourier University-Grenoble,

BP 166, 38042 Grenoble Cedex 9 , France

*e-mail : *atten@labs.polycnrs-gre.fr*
*

**D. Koulova-Nenova**

Institute of Mechanics, Bulgarian Academy of Sciences,

Acad. G. Bonchev Str, Bl. 4, 1113 Sofia, Bulgaria,

*e-mail: dantchi@imbm.bas.bg*

**TIME EVOLUTION OF A VISCOUS LIQUID JET BY ONE-DIMENSIONAL MODEL**

Abstract**.** We consider the general problem of the deformation of
a liquid jet. By imposing an axially periodic perturbation an approximate spatio-temporal
solution from the temporal evolution of a liquid cylinder is derived. We seek for a
numerical treatment retaining the non-linear aspects of the jet deformation, but which is
tractable enough to give solutions after a relatively limited amount of computational
efforts. The so-called one-dimensional model, taking into account the liquid viscosity
offers such a capability by retaining the essential aspects of the physical phenomenon.
This model gives the two equations for the evolution of the local jet radii *R(z,t)*
and the axial velocity perturbation *U(z,t)*. The technique used for solving the
partial differential equations in *z* and *t* is of Galerkin type, based on
expansions of all variables in Fourier series and on numerical determination of the terms
(like the pressure *P*), for which equations cannot be derived easily giving the time
evolution of the different Fourier components. This method is interesting for its easy and
direct comparison with some experimental results [1].

Key words: liquid jet, deformation, break-up

**Jozef Turza**

Slovak University of Technology,

01841 Dubnica nad Vahom, Slovakia,

e-mail: dpmtf@ztsdubnica.sk

**PROBLEMS STABILIZATION TWO PHASE HYDROSTATIC MECHANISM WITH THE FLUID
ALTERNATING FLOW (FAF)**

Abstract. The article deals with an analysis of the double-phase transmission with fluid alternating flow by means of the method known from mechatronical systems, i.e. by means of a computer-based simulation in the DYNAST environment. This method comes out from a consistent power interaction and the power flow between the object under investigation and the environment. Some results of this analysis are mentioned here with focusing to investigations of a central position of the hydraulic motor piston when applying various manners of loading.

Key words: fluid parallel flow, fluid alternating flow, mechatronical system, power interaction, equivalent circuit structure, resistances to power transfer, voltage sources, current supplies, transformers.

**R. Savova**

Institute of Mechanics, Bulgarian Academy of Sciences,

Acad. G. Bonchev Str., Bl.4, 1113 Sofia, Bulgaria,

*e mail: *radianka@imech.imbm.bas.bg

**ENERGY-FLUX VECTORS IN THERMOELASTICITY**

Abstract. The energy-flux vector in a thermoelastic medium could be defined in different ways, which lead to different results for the energy velocity. Of course these definitions coincide when the thermal effects are neglected. In this paper we consider two possible definitions for the energy-flux vector in thermoelasticity. Some numerical results are presented in order to compare these definitions for the case of surface waves in a half-space.

Key words: thermoelasticity, energy-flux vector, surface waves.

**R. P. Dobrev**

44, Bogdan Str., 1505 Sofia, Bulgaria,

*e-mail: *dobrev@intech.bg* *

**A MODEL OF A SUPPORTIVE LOAD-CARRYING STRATEGY MODULATING FORCES AND
STRESSES IN THE HUMAN ILIAC BONE AND FEMORAL NECK. PART II: MATHEMATICAL EVALUATION**

Abstract. A three dimensional force analysis, calculating not only the magnitude of the muscle forces but also the directions of their action, is presented. Thus, the directions of the fan-like muscles forces are not determined in advance. The method proposed provides the possibility of evaluating the activity of the supportive muscles described in Part I. The supportive function of these muscles is controlled by the central nervous system independently of their other dynamic functions. Thus it is not possible for the supportive activity of the muscles to be uncovered by routine biomechanical force analysis. The method proposed enables the forces produced by the supportive muscles to be described.

Key words: Biomechanics, hip joint, muscle force direction, acetabular contact force, femoral neck loading.

**N. Petrov**

Institute of Mechanics, Bulgarian Academy of Sciences,

Acad. G. Bonchev Str., Bl. 4, 1113 Sofia, Bulgaria,

*e-mail: nikolapetrov@dir.bg*

**S. R. Pollack**

Department of Bioengineering, University of Pennsylvania,

PA 19104-6392, U.S.A,

*e-mail: spollack@seas.upenn.edu*

**DRAINAGE DISTANCE OF STRESS INDUCED FLUID FLOW IN CORTICAL BONE**

Abstract. The aim of the present study is to estimate the drainage distance and the location of the fluid catchment zones by means of computational modelling of stress induced fluid flow in cortical bone. We study a system of osteons, which mimics the structure of a real specimen [3], using finite element method. The anatomical model consists of 40 randomly positioned osteons in a segment of a rectangular specimen undergoing 4-point bending so that the model is subjected to instantaneous pure bending. The process of relaxation of the fluid pressure is under consideration. The results demonstrate the formation of fluid catchment areas around the Haversian canals, and pressure extremes between osteons that result in no macroscopic flow nor exchange of fluid between the osteons. The computational results are also consistent with [9, 10], in which the obtained fluid pressure relaxation is independent of specimen thickness.

Key words: bone, petrov, pollack, biomechanics, fluid, flow, streaming, potential, remodelling, osteon.