The Two-Point Problem as the Mathematical Model of the Oscillation Process of a Longitudinal Body
The wave process of an elastic longitudinal body at given positions or speeds of change at two time moments is described by a mathematical model. The study of this model includes finding the solution of the partial differential equation of second order in
- PDF / 1,538,612 Bytes
- 11 Pages / 439.37 x 666.142 pts Page_size
- 45 Downloads / 173 Views
and Oksana Malanchuk2(B)
1 Lviv Polytechnic National University, Lviv 79013, Ukraine
[email protected] 2 Danylo Halytsky Lviv National Medical University, Lviv 79017, Ukraine
[email protected]
Abstract. The wave process of an elastic longitudinal body at given positions or speeds of change at two time moments is described by a mathematical model. The study of this model includes finding the solution of the partial differential equation of second order in time that satisfies two-point in time conditions. The method for constructing an analytical solution is developed. The examples of some oscillatory systems models are given and processes in them are studied. Keywords: Mathematical model · Oscillation propagation · Differential-symbol method · Two-point problem
1 Introduction The study of processes, systems and signals is possible on the basis of different approaches [1]. One of the directions of such research is the principle of mathematical modeling, which involves the study of an object based on its mathematical model. This approach makes it possible to study the system without experiment, which is impossible or extremely costly for various reasons (economic, technical, etc.); abstraction of the specific nature of the system, due to the fact that the same model often describes different processes and properties of the system, reflecting properties of the object which are most important in this case, ignoring unimportant properties; predicting results at the different factors and for the different parameters [2–4]. The mathematical models allow to classificate the systems, processes and signals, to compare them, to identify the similar or different elements.
2 Analysis of Problem The research of oscillatory phenomena in different systems is an important problem in mathematical modeling of such system. So, in modern technologies there is a need to introduce such advanced materials as nanotubes, which are a set of one-dimensional © The Author(s), under exclusive license to Springer Nature Switzerland AG 2021 N. Shakhovska and M. O. Medykovskyy (Eds.): CSIT 2020, AISC 1293, pp. 540–550, 2021. https://doi.org/10.1007/978-3-030-63270-0_36
The Two-Point Problem as the Mathematical Model of the Oscillation Process
541
carbon crystals. The simplest mathematical model of oscillatory processes in similar materials of these systems can be constructed on the basis of a chain of mathematical pendulums. It makes possible to study the vibrational spectrum of a crystal [5]. Oscillatory process is an essential component of systems of different nature. In particular, biological systems are the sum of oscillators [6]. Oscillatory processes in the human body provide the coordination of physiological processes with the maintenance of communication between individual parts of the system, as well as involved in the exchange of information [7]. Parameters of the oscillatory processes are important in the diagnosis of cardiovascular, nervous, visual, auditory and other human systems [8]. The neural oscillations wh
Data Loading...
