Mathematics of oscillations and waves

[摘要] Analytical definition of the sine function and the number π which is related to sine function allows to understand, how harmonic oscillations and waves appear. The functional equation for the sine is received. The new fast algorithm of calculation of the π number is formulated. In the elementary case oscillations and waves are harmonious or sinusoidal. The sine function appears not accidentally. This function can be defined as the solution of the functional equation characterizing periodic properties of oscillations and waves.

[发布机构] Bauman Moscow State Technical University, Moscow, Russia^1;S.I. Vavilov Institute of History of Science and Technology of the Russian Academy of Sciences, Moscow, Russia^2

[效力级别] 力学 [学科分类] 力学，机械学

[关键词] Fast algorithms;Functional equation;Harmonic oscillation;Periodic properties;Pi numbers;Sine functions