Abstract
In this paper we propose a new analytical approach to the study of human gait dynamics. A new and reliable method, namely the Optimal Auxiliary Functions Method (OAFM) is employed to obtain explicit and accurate analytical solutions. The capabilities of this new method are successfully tested in the studyof human gait dynamics and an excellent agreement between analytical and numerical solutions is demonstrated. The accuracy of the analytical results is assured by the so-called convergence-control parameters, whose optimal values are rigorously identified in order to provide a fast convergence to the exact solution.
Highlights
The dynamics of human gait is a topic of interest for scientists concerned with biomechanics
It is known that human walking is a consequence of the commands given by the central nervous system transmitted through the intraspinal nervous system to the mechanical periphery of the body, which consists of bones and muscles receiving commands
In this work, taking into consideration the model proposed in [7], we develop a new analytical approach to the study of human gait dynamic problems by means of a new analytical method, namely the Optimal Auxiliary Functions Method (OAFM), in order to test its applicability in this kind of problems
Summary
The dynamics of human gait is a topic of interest for scientists concerned with biomechanics. In order to briefly present the basics of the method employed in this study, namely the Optimal Auxiliary Functions Method (OAFM), we will take into consideration the most general form of a nonlinear differential equation It is well-known that an exact solution rarely happens to be identifiable for such an equation, so that in the frame of this method of solution, an approximate analytical solution will be proposed of the form u~(x, Ci ) u0 (x) u1(x, Ci ), i 1,2,..., s (5). The optimal values of the initially unknown convergence-control parameters should be identified using various rigorous methods, such as the Galerkin method, the least square method, the Ritz method, the collocation method and so on Knowing these optimal values of Ci and C j , the approximate analytical solution is explicitly obtained, so that this procedure proves to be a powerful tool for solving nonlinear and even strongly nonlinear problems
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