Impact of a Multiple Pendulum with a Non-Linear Contact Force

This article presents a method to solve the impact of a kinematic chain in terms of a non-linear contact force. The nonlinear contact force has different expressions for elastic compression, elasto-plastic compression, and elastic restitution. Lagrange equations of motion are used to obtain the non-...

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Bibliographic Details
Main Authors:	Dan B. Marghitu, Jing Zhao
Format:	Article
Language:	English
Published:	MDPI AG 2020-07-01
Series:	Mathematics
Subjects:	impact non-linear contact force friction force non-linear equations of motion permanent deformation
Online Access:	https://www.mdpi.com/2227-7390/8/8/1202

id	doaj-9e33e7b380b64b7e8d645207d670ba62
record_format	Article
spelling	doaj-9e33e7b380b64b7e8d645207d670ba622020-11-25T03:45:12ZengMDPI AGMathematics2227-73902020-07-0181202120210.3390/math8081202Impact of a Multiple Pendulum with a Non-Linear Contact ForceDan B. Marghitu0Jing Zhao1Department of Mechanical Engineering, 1418 Wiggins Hall, Auburn University, Auburn, AL 36849-5341, USADepartment of Mechanical Engineering, 1418 Wiggins Hall, Auburn University, Auburn, AL 36849-5341, USAThis article presents a method to solve the impact of a kinematic chain in terms of a non-linear contact force. The nonlinear contact force has different expressions for elastic compression, elasto-plastic compression, and elastic restitution. Lagrange equations of motion are used to obtain the non-linear equations of motion with friction for the collision period. The kinetic energy during the impact is compared with the pre-impact kinetic energy. During the impact of a double pendulum the kinetic energy of the non-impacting link is increasing and the total kinetic energy of the impacting link is decreasing.https://www.mdpi.com/2227-7390/8/8/1202impactnon-linear contact forcefriction forcenon-linear equations of motionpermanent deformation
collection	DOAJ
language	English
format	Article
sources	DOAJ
author	Dan B. Marghitu Jing Zhao
spellingShingle	Dan B. Marghitu Jing Zhao Impact of a Multiple Pendulum with a Non-Linear Contact Force Mathematics impact non-linear contact force friction force non-linear equations of motion permanent deformation
author_facet	Dan B. Marghitu Jing Zhao
author_sort	Dan B. Marghitu
title	Impact of a Multiple Pendulum with a Non-Linear Contact Force
title_short	Impact of a Multiple Pendulum with a Non-Linear Contact Force
title_full	Impact of a Multiple Pendulum with a Non-Linear Contact Force
title_fullStr	Impact of a Multiple Pendulum with a Non-Linear Contact Force
title_full_unstemmed	Impact of a Multiple Pendulum with a Non-Linear Contact Force
title_sort	impact of a multiple pendulum with a non-linear contact force
publisher	MDPI AG
series	Mathematics
issn	2227-7390
publishDate	2020-07-01
description	This article presents a method to solve the impact of a kinematic chain in terms of a non-linear contact force. The nonlinear contact force has different expressions for elastic compression, elasto-plastic compression, and elastic restitution. Lagrange equations of motion are used to obtain the non-linear equations of motion with friction for the collision period. The kinetic energy during the impact is compared with the pre-impact kinetic energy. During the impact of a double pendulum the kinetic energy of the non-impacting link is increasing and the total kinetic energy of the impacting link is decreasing.
topic	impact non-linear contact force friction force non-linear equations of motion permanent deformation
url	https://www.mdpi.com/2227-7390/8/8/1202
work_keys_str_mv	AT danbmarghitu impactofamultiplependulumwithanonlinearcontactforce AT jingzhao impactofamultiplependulumwithanonlinearcontactforce
_version_	1724510572946391040

Impact of a Multiple Pendulum with a Non-Linear Contact Force

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