The locus of the angular velocity vector of a moving rigid body is a cylindrical surface.
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| Title: | The locus of the angular velocity vector of a moving rigid body is a cylindrical surface. |
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| Authors: | Cervantes-Sánchez, J. Jesús1 (AUTHOR) jecer@ugto.mx, Rico-Martínez, José M.1 (AUTHOR), García-Murillo, Mario A.1 (AUTHOR), García-García, Ricardo1 (AUTHOR) |
| Source: | Mechanics Based Design of Structures & Machines. 2025, Vol. 53 Issue 6, p4812-4829. 18p. |
| Subjects: | Angular velocity, Angular acceleration, Acceleration (Mechanics), Gaussian elimination, Body image |
| Abstract: | This work presents a procedure that allows us to formulate logically and orderly all the equations of position, velocity, and acceleration that must be satisfied by any rigid body moving arbitrarily in three-dimensional physical space. Using Gaussian elimination, the complex system of linear equations can be changed to a more straightforward equivalent system of linearly independent equations, eliminating redundant equations and making the solution directly obtainable without much effort. This formulation allows us to systematically obtain the kinematic parameters of position, velocity, and acceleration associated with a rigid body in arbitrary motion, including the angular velocity vector and the angular acceleration vector. The particularity of the development allows us to find a unique condition that makes the position, velocity, and acceleration equations compatible. This condition gives rise to a novel and original symbolic equation representing a cylindrical surface whose points represent the locus of the angular velocity vector of the rigid body in motion. Two fully detailed case studies illustrate the applicability of the discovery. This research may help estimate a rigid body's attitude and use accelerometers to control machines, mechanisms, and robots moving in space. [ABSTRACT FROM AUTHOR] |
| Copyright of Mechanics Based Design of Structures & Machines is the property of Taylor & Francis Ltd and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.) | |
| Database: | Engineering Source |
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| Header | DbId: egs DbLabel: Engineering Source An: 185527887 AccessLevel: 6 PubType: Academic Journal PubTypeId: academicJournal PreciseRelevancyScore: 0 |
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| Items | – Name: Title Label: Title Group: Ti Data: The locus of the angular velocity vector of a moving rigid body is a cylindrical surface. – Name: Author Label: Authors Group: Au Data: <searchLink fieldCode="AR" term="%22Cervantes-Sánchez%2C+J%2E+Jesús%22">Cervantes-Sánchez, J. Jesús</searchLink><relatesTo>1</relatesTo> (AUTHOR)<i> jecer@ugto.mx</i><br /><searchLink fieldCode="AR" term="%22Rico-Martínez%2C+José+M%2E%22">Rico-Martínez, José M.</searchLink><relatesTo>1</relatesTo> (AUTHOR)<br /><searchLink fieldCode="AR" term="%22García-Murillo%2C+Mario+A%2E%22">García-Murillo, Mario A.</searchLink><relatesTo>1</relatesTo> (AUTHOR)<br /><searchLink fieldCode="AR" term="%22García-García%2C+Ricardo%22">García-García, Ricardo</searchLink><relatesTo>1</relatesTo> (AUTHOR) – Name: TitleSource Label: Source Group: Src Data: <searchLink fieldCode="JN" term="%22Mechanics+Based+Design+of+Structures+%26+Machines%22">Mechanics Based Design of Structures & Machines</searchLink>. 2025, Vol. 53 Issue 6, p4812-4829. 18p. – Name: Subject Label: Subjects Group: Su Data: <searchLink fieldCode="DE" term="%22Angular+velocity%22">Angular velocity</searchLink><br /><searchLink fieldCode="DE" term="%22Angular+acceleration%22">Angular acceleration</searchLink><br /><searchLink fieldCode="DE" term="%22Acceleration+%28Mechanics%29%22">Acceleration (Mechanics)</searchLink><br /><searchLink fieldCode="DE" term="%22Gaussian+elimination%22">Gaussian elimination</searchLink><br /><searchLink fieldCode="DE" term="%22Body+image%22">Body image</searchLink> – Name: Abstract Label: Abstract Group: Ab Data: This work presents a procedure that allows us to formulate logically and orderly all the equations of position, velocity, and acceleration that must be satisfied by any rigid body moving arbitrarily in three-dimensional physical space. Using Gaussian elimination, the complex system of linear equations can be changed to a more straightforward equivalent system of linearly independent equations, eliminating redundant equations and making the solution directly obtainable without much effort. This formulation allows us to systematically obtain the kinematic parameters of position, velocity, and acceleration associated with a rigid body in arbitrary motion, including the angular velocity vector and the angular acceleration vector. The particularity of the development allows us to find a unique condition that makes the position, velocity, and acceleration equations compatible. This condition gives rise to a novel and original symbolic equation representing a cylindrical surface whose points represent the locus of the angular velocity vector of the rigid body in motion. Two fully detailed case studies illustrate the applicability of the discovery. This research may help estimate a rigid body's attitude and use accelerometers to control machines, mechanisms, and robots moving in space. [ABSTRACT FROM AUTHOR] – Name: AbstractSuppliedCopyright Label: Group: Ab Data: <i>Copyright of Mechanics Based Design of Structures & Machines is the property of Taylor & Francis Ltd and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.) |
| PLink | https://search.ebscohost.com/login.aspx?direct=true&site=eds-live&db=egs&AN=185527887 |
| RecordInfo | BibRecord: BibEntity: Identifiers: – Type: doi Value: 10.1080/15397734.2025.2456645 Languages: – Code: eng Text: English PhysicalDescription: Pagination: PageCount: 18 StartPage: 4812 Subjects: – SubjectFull: Angular velocity Type: general – SubjectFull: Angular acceleration Type: general – SubjectFull: Acceleration (Mechanics) Type: general – SubjectFull: Gaussian elimination Type: general – SubjectFull: Body image Type: general Titles: – TitleFull: The locus of the angular velocity vector of a moving rigid body is a cylindrical surface. Type: main BibRelationships: HasContributorRelationships: – PersonEntity: Name: NameFull: Cervantes-Sánchez, J. Jesús – PersonEntity: Name: NameFull: Rico-Martínez, José M. – PersonEntity: Name: NameFull: García-Murillo, Mario A. – PersonEntity: Name: NameFull: García-García, Ricardo IsPartOfRelationships: – BibEntity: Dates: – D: 01 M: 06 Text: 2025 Type: published Y: 2025 Identifiers: – Type: issn-print Value: 15397734 Numbering: – Type: volume Value: 53 – Type: issue Value: 6 Titles: – TitleFull: Mechanics Based Design of Structures & Machines Type: main |
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