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    On the Quasi-Diagonalization and Uncoupling of Gyroscopic Circulatory Multi-Degree-of-Freedom Systems

    Source: Journal of Applied Mechanics:;2024:;volume( 092 ):;issue: 002::page 21005-1
    Author:
    Bulatovic, Ranislav M.
    ,
    Udwadia, Firdaus E.
    DOI: 10.1115/1.4067148
    Publisher: The American Society of Mechanical Engineers (ASME)
    Abstract: A new central result that gives the necessary and sufficient conditions for two n by n skew-symmetric matrices and one symmetric matrix to be simultaneously quasi-diagonalized by a real orthogonal congruence is proved. Based on this result, the decomposition of linear multi-degree-of-freedom dynamical systems with gyroscopic, circulatory, and potential forces is investigated through a real linear coordinate transformation generated by an orthogonal matrix. Several sets of conditions, applicable to real-life structural and mechanical systems arising in aerospace, civil, and mechanical engineering, under which such a coordinate transformation exists are found, thereby allowing these systems to be decomposed into independent, uncoupled subsystems, each with a maximum of two degrees of freedom. The conditions are expressed in terms of the coefficient matrices of the system. A specific form for the circulatory (gyroscopic) matrix is posited, and when the gyroscopic (circulatory) matrix is simple—a situation that commonly appears in real-life applications—it is shown that just a single necessary and sufficient condition is required for the decomposition of the multi-degree-of-freedom system. Numerical examples are provided throughout to demonstrate the analytical results.
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      On the Quasi-Diagonalization and Uncoupling of Gyroscopic Circulatory Multi-Degree-of-Freedom Systems

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    http://yetl.yabesh.ir/yetl1/handle/yetl/4305227
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    contributor authorBulatovic, Ranislav M.
    contributor authorUdwadia, Firdaus E.
    date accessioned2025-04-21T09:58:30Z
    date available2025-04-21T09:58:30Z
    date copyright12/17/2024 12:00:00 AM
    date issued2024
    identifier issn0021-8936
    identifier otherjam_92_2_021005.pdf
    identifier urihttp://yetl.yabesh.ir/yetl1/handle/yetl/4305227
    description abstractA new central result that gives the necessary and sufficient conditions for two n by n skew-symmetric matrices and one symmetric matrix to be simultaneously quasi-diagonalized by a real orthogonal congruence is proved. Based on this result, the decomposition of linear multi-degree-of-freedom dynamical systems with gyroscopic, circulatory, and potential forces is investigated through a real linear coordinate transformation generated by an orthogonal matrix. Several sets of conditions, applicable to real-life structural and mechanical systems arising in aerospace, civil, and mechanical engineering, under which such a coordinate transformation exists are found, thereby allowing these systems to be decomposed into independent, uncoupled subsystems, each with a maximum of two degrees of freedom. The conditions are expressed in terms of the coefficient matrices of the system. A specific form for the circulatory (gyroscopic) matrix is posited, and when the gyroscopic (circulatory) matrix is simple—a situation that commonly appears in real-life applications—it is shown that just a single necessary and sufficient condition is required for the decomposition of the multi-degree-of-freedom system. Numerical examples are provided throughout to demonstrate the analytical results.
    publisherThe American Society of Mechanical Engineers (ASME)
    titleOn the Quasi-Diagonalization and Uncoupling of Gyroscopic Circulatory Multi-Degree-of-Freedom Systems
    typeJournal Paper
    journal volume92
    journal issue2
    journal titleJournal of Applied Mechanics
    identifier doi10.1115/1.4067148
    journal fristpage21005-1
    journal lastpage21005-13
    page13
    treeJournal of Applied Mechanics:;2024:;volume( 092 ):;issue: 002
    contenttypeFulltext
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