Relation between posicast-shaped function and vibration manipulation function of undamped 1-DOF linear oscillator for one-time rest-to-rest motion in a natural period

Although more than 55 years have been passed since its first development, it remains unknown whether a posicast-shaped function (PSF) is a unique intermittent input command for a one-time rapid rest-to-rest motion in one natural period. In addition, it has not been determined whether more generalize...

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Autores principales:	Shigeo KOTAKE, Ryo ICHIZAKI
Formato:	article
Lenguaje:	EN
Publicado:	The Japan Society of Mechanical Engineers 2017
Materias:	posicast shaping input shaping rapid rest-to-rest motion vibration manipulation function Mechanical engineering and machinery TJ1-1570
Acceso en línea:	https://doaj.org/article/4a9d47af15e24c7e81a20690357106a8
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spelling	oai:doaj.org-article:4a9d47af15e24c7e81a20690357106a82021-11-26T07:06:29ZRelation between posicast-shaped function and vibration manipulation function of undamped 1-DOF linear oscillator for one-time rest-to-rest motion in a natural period2187-974510.1299/mej.17-00031https://doaj.org/article/4a9d47af15e24c7e81a20690357106a82017-06-01T00:00:00Zhttps://www.jstage.jst.go.jp/article/mej/4/4/4_17-00031/_pdf/-char/enhttps://doaj.org/toc/2187-9745Although more than 55 years have been passed since its first development, it remains unknown whether a posicast-shaped function (PSF) is a unique intermittent input command for a one-time rapid rest-to-rest motion in one natural period. In addition, it has not been determined whether more generalized expressions exist. We recently deduced an intermittent input command of a feedforward formula, called a vibration manipulation function for one natural period (oVMF), to manipulate an undamped 1-DOF linear floating oscillator in an arbitral operational period based on the dynamics of three vibro-impact oscillators under a Grover algorithm in the field of quantum information. As a special case of oVMF, we can define the formula of an input command for a rest-to-rest motion in one natural period, called roVMF. In this study, we proved that any PSF for an undamped 1-DOF oscillator (uPSF) can be expressed as an infinite series of roVMF. Moreover, because uPSF has a stricter symmetrical property than roVMF, we have concluded that the set of uPSF, Uup, is contained in the set of roVMF, UroV. Hence roVMF is a more general expression than uPSF.Shigeo KOTAKERyo ICHIZAKIThe Japan Society of Mechanical Engineersarticleposicast shapinginput shapingrapid rest-to-rest motionvibration manipulation functionMechanical engineering and machineryTJ1-1570ENMechanical Engineering Journal, Vol 4, Iss 4, Pp 17-00031-17-00031 (2017)
institution	DOAJ
collection	DOAJ
language	EN
topic	posicast shaping input shaping rapid rest-to-rest motion vibration manipulation function Mechanical engineering and machinery TJ1-1570
spellingShingle	posicast shaping input shaping rapid rest-to-rest motion vibration manipulation function Mechanical engineering and machinery TJ1-1570 Shigeo KOTAKE Ryo ICHIZAKI Relation between posicast-shaped function and vibration manipulation function of undamped 1-DOF linear oscillator for one-time rest-to-rest motion in a natural period
description	Although more than 55 years have been passed since its first development, it remains unknown whether a posicast-shaped function (PSF) is a unique intermittent input command for a one-time rapid rest-to-rest motion in one natural period. In addition, it has not been determined whether more generalized expressions exist. We recently deduced an intermittent input command of a feedforward formula, called a vibration manipulation function for one natural period (oVMF), to manipulate an undamped 1-DOF linear floating oscillator in an arbitral operational period based on the dynamics of three vibro-impact oscillators under a Grover algorithm in the field of quantum information. As a special case of oVMF, we can define the formula of an input command for a rest-to-rest motion in one natural period, called roVMF. In this study, we proved that any PSF for an undamped 1-DOF oscillator (uPSF) can be expressed as an infinite series of roVMF. Moreover, because uPSF has a stricter symmetrical property than roVMF, we have concluded that the set of uPSF, Uup, is contained in the set of roVMF, UroV. Hence roVMF is a more general expression than uPSF.
format	article
author	Shigeo KOTAKE Ryo ICHIZAKI
author_facet	Shigeo KOTAKE Ryo ICHIZAKI
author_sort	Shigeo KOTAKE
title	Relation between posicast-shaped function and vibration manipulation function of undamped 1-DOF linear oscillator for one-time rest-to-rest motion in a natural period
title_short	Relation between posicast-shaped function and vibration manipulation function of undamped 1-DOF linear oscillator for one-time rest-to-rest motion in a natural period
title_full	Relation between posicast-shaped function and vibration manipulation function of undamped 1-DOF linear oscillator for one-time rest-to-rest motion in a natural period
title_fullStr	Relation between posicast-shaped function and vibration manipulation function of undamped 1-DOF linear oscillator for one-time rest-to-rest motion in a natural period
title_full_unstemmed	Relation between posicast-shaped function and vibration manipulation function of undamped 1-DOF linear oscillator for one-time rest-to-rest motion in a natural period
title_sort	relation between posicast-shaped function and vibration manipulation function of undamped 1-dof linear oscillator for one-time rest-to-rest motion in a natural period
publisher	The Japan Society of Mechanical Engineers
publishDate	2017
url	https://doaj.org/article/4a9d47af15e24c7e81a20690357106a8
work_keys_str_mv	AT shigeokotake relationbetweenposicastshapedfunctionandvibrationmanipulationfunctionofundamped1doflinearoscillatorforonetimeresttorestmotioninanaturalperiod AT ryoichizaki relationbetweenposicastshapedfunctionandvibrationmanipulationfunctionofundamped1doflinearoscillatorforonetimeresttorestmotioninanaturalperiod
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Relation between posicast-shaped function and vibration manipulation function of undamped 1-DOF linear oscillator for one-time rest-to-rest motion in a natural period

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