On Bessel's functions of several variables and their applications in mechanics
Abstract
The subject of the present work is the study of functions which initially appear in the form of a definite integral (see the article). In the special case of a single variable, we have the classical Kepler equation and its solution given by Bessel. As a simplest example illustrating the application of the obtained formulas, I present the classical problem of the motion of a spherical pendulum in the case of its small oscillations about the lowest equilibrium position. As examples of the application of generalized Bessel functions, I also present the equation of the mathematical pendulum, the equation of the theory of longitudinal bending, the differential equation encountered in the theory of small oscillations in a vacuum of a system with one degree of freedom, as well as in many recent investigations in celestial mechanics, and the differential equation of small oscillations in a resisting medium when the resistance of the medium is proportional to the square of the velocity.
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