Results on singular products of the distributions $x_{\pm }^{-p}$ and $x^{-p}$ for natural $p$ are derived, when the products are balanced so that their sum exists in the distribution space. These results follow the pattern of a known distributional product published by Jan Mikusiński in 1966. The results are obtained in the Colombeau algebra of generalized functions, which is the most relevant algebraic construction for tackling nonlinear problems of Schwartz distributions.
Let $P_k$ denote a path with $k$ edges and $łK_{n,n}$ denote the $ł$-fold complete bipartite graph with both parts of size $n$. In this paper, we obtain the necessary and sufficient conditions for $łK_{n,n}$ to have a balanced $P_k$-decomposition. We also obtain the directed version of this result.
The paper deals with the modelling of balancing machine vibration and the identifícation of the stiffness and damping coefficients of oil-film bearings. The real balancing machine consists of a flexible rotor, oil-film bearings and bearing heads on spring elements. The mathematical model enables to calculate eigenvalues, critical revolutions and unbalance vibrations in dependence on the rotational speed. The identification method of the oil-film bearing stiffness and damping matrices is based on the minimization of differences between measured and calculated rotor critical speeds and bearing head displacements in balancing machines. The rotor is excited by attached known trial masses fixed in chosen balancing planes. and Obsahuje seznam literatury
This paper deals with the modelling and control of balanced wheeled autonomous mobile robot. For the MBS dynamics modelling software tool Matlab-SimMechanics is used. The model derived automatically from geometric-topological description of MBS is used for the control purposes (local linearization for state space control, testing of nonlinear system controlled by LQR) and also as a reference during the analytical model formulation for global feedback linearization. The dual accelerometer is used as a tilt sensor and the proposed method for sensory processing is described in this paper. The approach is based on iterative solution of nonlinear equation. Control using the state space (LQR) and the feedback linearization is compared. Also, the influence of sensor noises and delays implemented into the model are discussed. Finally, the solution is verified on real physical model controlled by means of hardware ni the loop (HIL). and Obsahuje seznam literatury