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Understanding the physics of eigenvalue-eigenfunction problems: Rotating beam problem.

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Title: Understanding the physics of eigenvalue-eigenfunction problems: Rotating beam problem.
Authors: Pakdemirli, Mehmet1 (AUTHOR) pakdemirli@gmail.com
Source: International Journal of Mechanical Engineering Education. Oct2025, Vol. 53 Issue 4, p795-807. 13p.
Subjects: Eigenvalues, Eigenfunctions, Differential equations, Mechanics (Physics), Rigid dynamics, Interpretation (Philosophy)
Abstract: Eigenvalue-eigenfunction problems frequently appear in many physical areas. Some mathematical experience is needed to identify whether the differential system is an eigenvalue-eigenfunction problem or not. Apart from the mathematical nature of the problem, the eigenvalue-eigenfunction solutions have physical interpretations which have to be addressed properly for real problems. The rotating beam problem is treated to exploit the mathematical and physical nature of such problems and the conditions to divert from the eigenvalue-eigenfunction problem. The rotation of a beam about its symmetry axis along its length and about another axis parallel to its symmetry axis changes the nature of the problem. While the former is an eigenvalue-eigenfunction problem, the latter is not. The interpretations of the physical consequences of the solutions are discussed in detail. The problem can be used as supplementary material in undergraduate courses such as differential equations, mechanics and dynamics. [ABSTRACT FROM AUTHOR]
Copyright of International Journal of Mechanical Engineering Education is the property of Sage Publications Inc. 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.)
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  Data: Understanding the physics of eigenvalue-eigenfunction problems: Rotating beam problem.
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  Data: <searchLink fieldCode="AR" term="%22Pakdemirli%2C+Mehmet%22">Pakdemirli, Mehmet</searchLink><relatesTo>1</relatesTo> (AUTHOR)<i> pakdemirli@gmail.com</i>
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  Data: <searchLink fieldCode="JN" term="%22International+Journal+of+Mechanical+Engineering+Education%22">International Journal of Mechanical Engineering Education</searchLink>. Oct2025, Vol. 53 Issue 4, p795-807. 13p.
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  Data: <searchLink fieldCode="DE" term="%22Eigenvalues%22">Eigenvalues</searchLink><br /><searchLink fieldCode="DE" term="%22Eigenfunctions%22">Eigenfunctions</searchLink><br /><searchLink fieldCode="DE" term="%22Differential+equations%22">Differential equations</searchLink><br /><searchLink fieldCode="DE" term="%22Mechanics+%28Physics%29%22">Mechanics (Physics)</searchLink><br /><searchLink fieldCode="DE" term="%22Rigid+dynamics%22">Rigid dynamics</searchLink><br /><searchLink fieldCode="DE" term="%22Interpretation+%28Philosophy%29%22">Interpretation (Philosophy)</searchLink>
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  Data: Eigenvalue-eigenfunction problems frequently appear in many physical areas. Some mathematical experience is needed to identify whether the differential system is an eigenvalue-eigenfunction problem or not. Apart from the mathematical nature of the problem, the eigenvalue-eigenfunction solutions have physical interpretations which have to be addressed properly for real problems. The rotating beam problem is treated to exploit the mathematical and physical nature of such problems and the conditions to divert from the eigenvalue-eigenfunction problem. The rotation of a beam about its symmetry axis along its length and about another axis parallel to its symmetry axis changes the nature of the problem. While the former is an eigenvalue-eigenfunction problem, the latter is not. The interpretations of the physical consequences of the solutions are discussed in detail. The problem can be used as supplementary material in undergraduate courses such as differential equations, mechanics and dynamics. [ABSTRACT FROM AUTHOR]
– Name: AbstractSuppliedCopyright
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  Data: <i>Copyright of International Journal of Mechanical Engineering Education is the property of Sage Publications Inc. 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.)
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        Text: English
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      – SubjectFull: Differential equations
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              Text: Oct2025
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