Abstract. This paper deals with the description of a theoretical background of systematic computer algebra methods for analyzing the realtime dynamics of robots with a large numbers of joints. Many numerical methods based on different principles of mechanics were developed to obtain the equations that model the dynamic behavior of robots. In this paper, the efficiency of computer algebra application was compared with the most popular methods of forming the dynamic equations of robots in real time. To this end, the computer algebra system VIBRAN was used. A real-time dynamic model in closed form of the robots with large numbers of joints has been developed, using the computer algebra technique with the following automatic program code generation.

Abstract. The aim of this paper is to describe a theoretical background of systematic computer algebra methods for analyzing the free and steady-state periodic vibrations of the nonlinear structures. Many analytical steady-state solution methods are developed but each of them has different capabilities. On the other hand, it is very important to assess the efficiency of analytical methods in terms of the computer algebra system. For this reason, the computer algebra system VIBRAN was used. In this paper, the efficiency of two analytical methods is assessed from the standpoint of the computer algebra system.

Abstract. The aim of this paper is to simplify numerical simulation of robots with a large number of joints. Many numerical methods based on different principles of mechanics are developed to obtain the equations that model the dynamic behavior of robots. In this paper, the efficiency of computer algebra application was compared with the most popular methods of forming the generalized inertia matrix of robots. To this end, the computer algebra system was used. Expressions for the generalized inertia matrix of the robots with a large number of joints have been derived, using the computer algebra technique with the following automatic program code generation. As shown in the paper, such an application could drastically reduce the number of floating point product operations, needed for efficient numerical simulation of robots.

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This paper deals with the description of a theoretical background of systematic computer algebra methods for the formation of structural matrices of piezoceramic finite elements. The efficiency of computer algebra application was compared here with the numerical integration methods of forming the structural matrices of the finite elements. To this end, the computer algebra system VIBRAN was used. Two popular finite elements for modelling piezoceramic actuators of the sector-type and the triangular one are discussed. All structural matrices of the elements were derived, using the computer algebra technique with the following automatic program code generation.