Experimental determining of distributions of pulses forcing a linear system, where pulse amplitudes and occurrence instants are random values, is burdened with errors resulting from uncertainty of the measurement and the differences between the model and the physical phenomenon. The objective of this work is an attempt to minimize these errors through application of an approximation algorithm that allows to determine parameters of response of the system to a single pulse forcing. The conclusions issuing from the investigations indicate that the parameters of the vibrating system should be selected so that the impact of the local deformations that occur while the system is being forced on the parameters of the system response should be as small as possible.
The ground-state configurations of the classical point-charge particles were calculated using a new genetic-algorithm-based approach. The structures obtained confirmed the recent Monte Carlo findings, including the metastable states.
Solving a stochastic problem for systems subjected to random series of pulses is, in the present case, aimed at determining of an approximate distribution of amplitudes of random pulses forcing vibrations of an oscillator with damping. The applied model of investigations indicated the source of difficulties connected with interpretation of the obtained results. Another issue discussed in the paper is how a change of the damping coefficient b of the system may result in a decrease of the difference between the actual distribution of random pulses and that determined from the waveform.
This paper investigates perturbation to the Noether symmetry of discrete holonomic nonconservative dynamical systems on a uniform lattice. Firstly, we give the Noether theorem of system. Secondly, both criterion of perturbation to the Noether symmetry and the Noether adiabatic invariants of system are obtained. Finally, an example is given to illustrate these results.
The perturbation to the Noether symmetry and the Noether adiabatic invariants of discrete difference variational Hamilton systems are investigated. The discrete the Noether exact invariant induced directly by the the Noether symmetry of the system without perturbation is given. The concept of discrete high-order adiabatic invariant is presented, the criterion of the perturbation to the Noether symmetry is established, and the discrete the Noether adiabatic invariant induced directly by the perturbation to the Noether symmetry is obtained. Lastly, an example is discussed to illustrate the application of the results.
The paper presents another phase of the study aimed at determining distributions of random pulses forcing vibration of an oscillator with damping. At this stage, the impact of the pulses amplitudes on distributions determined in a finite time interval is discussed. Application of a mathematical model in simulations allows to determine the differences between the distributions generated in MATLAB environment and those determined by a function. The experiment was designed so that the qualitative analysis of the issue was possible.
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