Abstract
A mathematical model of a travelling wave in a matrix form is constructed. A degree of discreteness of the travelling wave and corresponding steps in phase and length are introduced. Asymmetric, unified matrices are compiled, which represent a generalized travelling wave, depending on a degree of discreteness. A generalized, dimensionless travelling wave is transformed into a required one with dimensions by specified technical parameters: amplitude and wavelength that is realized. A dependency of coordinates of points of a plane discrete travelling wave and discrete phase angles is established. A dependency of angular (phase) velocity and velocity of the travelling wave, which corresponds to the known results, is established. The presented matrix mathematical model is considered as an initial stage of technical possibility to realize a continuous travelling wave in a discrete form when developing a new type of transportation – wave transport.
Highlights
IntroductionThe leading countries are actively pursuing research and development of new types of transportation, based on usage of different physical principles of movement and realized in many design schemes, in order to solve global environmental problems
The presented matrix mathematical model is considered as an initial stage of technical possibility to realize a continuous travelling wave in a discrete form when developing a new type of transportation – wave transport
A discrete mathematical model of the travelling wave is suggested in order to ensure a technical possibility of its realization in the development of a new type of conveyor transport
Summary
The leading countries are actively pursuing research and development of new types of transportation, based on usage of different physical principles of movement and realized in many design schemes, in order to solve global environmental problems. Such types of transportation include conveyor transport and its constructive realization in forms of a belt [15, 17, 19,20, 34], steel plate, roller, screw conveyor [39], multi-mass vibrating transporters of various modifications, including linear, spiral [40], pneumatic transport and its modern realization in a form of Hyperloop [41]. Various aspects of the mathematical theory of gravitational waves on a surface of an incompressible heavy fluid and practical applications
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