Single-joint spherical pendulum mathematical modeling in spherical coordinate system

Authors: Zaika V.V., Maslennikov A.L.
Published in issue: #9(38)/2019
DOI: 10.18698/2541-8009-2019-9-522
Category: Mechanics | Chapter: Biomechanics
Keywords: spherical pendulum, mathematical spherical pendulum, physical spherical pendulum, dissipation, modeling, mathematical model, numerical ODE integration, Runge-Kutta method
Published: 17.09.2019

Mathematical model of the n-link spherical pendulum could be used as a mathematical model of a single or a n-link human joint. Depending on practical problem formulation spherical pendulum could be considered as mathematical pendulum or as physical pendulum, where the last one is the more adequate model of a human joint. Consequently, the derivation of such mathematical models is required. In this paper the derivation of mathematical model of the mathematical and the physical single-joint spherical pendulum in spherical coordinate system is shown. Two cases are considered for both systems: without and with dissipation. Numerical simulation is realized utilizing explicit Runge-Kutta 4-th order method.

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