Modelling Human Gait using a Nonlinear Differential Equation

Jelena Schmalz; David Paul; Kathleen Shorter; Xenia Schmalz; Matthew Cooper; Aron Murphy

doi:10.1101/2021.03.16.435713

Modelling Human Gait using a Nonlinear Differential Equation

Jelena Schmalz
, David Paul
, Kathleen Shorter
, Xenia Schmalz
, Matthew Cooper
, Aron Murphy

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

Abstract

We introduce an innovative method for the investigation of human gait, which is based on the visualisation of the vertical component of the movement of the centre of mass during walking or running, in the space of the coordinates position, velocity, and acceleration of the centre of mass. We collected data and numerically approximated the gait by the best-fitting curve for a non-linear model. The resulting equation for the best fitting plane or curve in this space is a differential equation of second order. The model that we suggest is a Duffing equation with coefficients that depend on the height of a walker or runner and on the angular frequency of the oscillation. We present statistical analyses of the distribution of the Duffing stiffness depending on the speed.

Original language	English
Title of host publication	The 16th Australasian Conference on Mathematics and Computers in Sport Proceedings
Editors	Ray Stefani, Adrian Schembri
Publisher	ANZIAM Mathsport
Pages	93-102
Volume	16
DOIs	https://doi.org/10.1101/2021.03.16.435713
Publication status	Published - 9 Jul 2022
Event	16th Australasian Conference on Mathematics and Computers in Sport (ANZIAM Mathsport 2022) - Victoria University, Melbourne, Melbourne, Australia Duration: 7 Jul 2022 → 9 Jul 2022

Conference

Conference	16th Australasian Conference on Mathematics and Computers in Sport (ANZIAM Mathsport 2022)
City	Melbourne, Australia
Period	7/07/22 → 9/07/22

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10.1101/2021.03.16.435713

https://hdl.handle.net/1959.11/56336

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@inproceedings{56b141d90e574ac3bf457762a8cc73c2,

title = "Modelling Human Gait using a Nonlinear Differential Equation",

abstract = "We introduce an innovative method for the investigation of human gait, which is based on the visualisation of the vertical component of the movement of the centre of mass during walking or running, in the space of the coordinates position, velocity, and acceleration of the centre of mass. We collected data and numerically approximated the gait by the best-fitting curve for a non-linear model. The resulting equation for the best fitting plane or curve in this space is a differential equation of second order. The model that we suggest is a Duffing equation with coefficients that depend on the height of a walker or runner and on the angular frequency of the oscillation. We present statistical analyses of the distribution of the Duffing stiffness depending on the speed.",

author = "Jelena Schmalz and David Paul and Kathleen Shorter and Xenia Schmalz and Matthew Cooper and Aron Murphy",

year = "2022",

month = jul,

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doi = "10.1101/2021.03.16.435713",

language = "English",

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pages = "93--102",

editor = "Ray Stefani and Adrian Schembri",

booktitle = "The 16th Australasian Conference on Mathematics and Computers in Sport Proceedings",

publisher = "ANZIAM Mathsport",

note = "16th Australasian Conference on Mathematics and Computers in Sport (ANZIAM Mathsport 2022) ; Conference date: 07-07-2022 Through 09-07-2022",

}

Schmalz, J, Paul, D, Shorter, K, Schmalz, X, Cooper, M & Murphy, A 2022, Modelling Human Gait using a Nonlinear Differential Equation. in R Stefani & A Schembri (eds), The 16th Australasian Conference on Mathematics and Computers in Sport Proceedings. vol. 16, ANZIAM Mathsport, pp. 93-102, 16th Australasian Conference on Mathematics and Computers in Sport (ANZIAM Mathsport 2022), Melbourne, Australia, 7/07/22. https://doi.org/10.1101/2021.03.16.435713

Modelling Human Gait using a Nonlinear Differential Equation. / Schmalz, Jelena; Paul, David; Shorter, Kathleen et al.
The 16th Australasian Conference on Mathematics and Computers in Sport Proceedings. ed. / Ray Stefani; Adrian Schembri. Vol. 16 ANZIAM Mathsport, 2022. p. 93-102.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

TY - GEN

T1 - Modelling Human Gait using a Nonlinear Differential Equation

AU - Schmalz, Jelena

AU - Paul, David

AU - Shorter, Kathleen

AU - Schmalz, Xenia

AU - Cooper, Matthew

AU - Murphy, Aron

PY - 2022/7/9

Y1 - 2022/7/9

N2 - We introduce an innovative method for the investigation of human gait, which is based on the visualisation of the vertical component of the movement of the centre of mass during walking or running, in the space of the coordinates position, velocity, and acceleration of the centre of mass. We collected data and numerically approximated the gait by the best-fitting curve for a non-linear model. The resulting equation for the best fitting plane or curve in this space is a differential equation of second order. The model that we suggest is a Duffing equation with coefficients that depend on the height of a walker or runner and on the angular frequency of the oscillation. We present statistical analyses of the distribution of the Duffing stiffness depending on the speed.

AB - We introduce an innovative method for the investigation of human gait, which is based on the visualisation of the vertical component of the movement of the centre of mass during walking or running, in the space of the coordinates position, velocity, and acceleration of the centre of mass. We collected data and numerically approximated the gait by the best-fitting curve for a non-linear model. The resulting equation for the best fitting plane or curve in this space is a differential equation of second order. The model that we suggest is a Duffing equation with coefficients that depend on the height of a walker or runner and on the angular frequency of the oscillation. We present statistical analyses of the distribution of the Duffing stiffness depending on the speed.

UR - https://www.anziam.org.au/MathSport+Proceedings

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DO - 10.1101/2021.03.16.435713

M3 - Conference contribution

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BT - The 16th Australasian Conference on Mathematics and Computers in Sport Proceedings

A2 - Stefani, Ray

A2 - Schembri, Adrian

PB - ANZIAM Mathsport

T2 - 16th Australasian Conference on Mathematics and Computers in Sport (ANZIAM Mathsport 2022)

Y2 - 7 July 2022 through 9 July 2022

ER -

Modelling Human Gait using a Nonlinear Differential Equation

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