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ASME International
On the Equations of Motion for Constrained Systems and Their Stability
Ranislav M. Bulatovic , Firdaus E. Udwadia
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2026
Abstract This paper presents recent advances and reviews several notions on constrained systems that have evolved over the years. It questions several of the ‘received (conventional) views’ on both holonomic and non-holonomic systems and shows their erroneous nature in light of recent developments. By using simple illustrative examples, it draws attention to several key ideas that differ from conventional views on the behavior of constrained systems, and especially their stability. Using the explicit equation of motion for constrained systems, we show that an degree of freedom unconstrained dynamical system upon which holonomic and/or nonholonomic constraints are imposed, remains an n degree of freedom system with the initial conditions allowed by the constraints. A central result on the stability of systems using the explicit equation is developed. It encompasses holonomic and/or nonholonomic constraints, including a wide class of nonlinear nonholonomic constraints. Several commonly held notions related to constrained systems are examined and found to require refinement, alteration, or rejection.
ASME International
On the Equations of Motion for Constrained Systems and Their Stability
Abstract This paper presents recent advances and reviews several notions on constrained systems that have evolved over the years. It questions several of the ‘received (conventional) views’ on both holonomic and non-holonomic systems and shows their erroneous nature in light of recent developments. By using simple illustrative examples, it draws attention to several key ideas that differ from conventional views on the behavior of constrained systems, and especially their stability....
Download 2026 Ranislav M. Bulatovic , Firdaus E. Udwadia
ASME International
Uncoupling of General Linear Multi-degree-of-freedom Structural and Mechanical Systems Through Quasi-diagonalization
Abstract This paper develops a fundamental result in linear algebra by providing the necessary and sufficient conditions for the simultaneous quasi-diagonalization of two symmetric matrices and two skew-symmetric matrices by a real orthogonal congruence. This result is used to study the uncoupling of general linear multi-degree-of-freedom (MDOF) structural and mechanical systems described by arbitrary damping and stiffness matrices through quasi-diagonalization, and real orthogonal...
Download 2025 Ranislav M. Bulatovic , Firdaus E. Udwadia
ASME International
Uncoupling of Damped Linear Potential Multi-Degrees-of-Freedom Structural and Mechanical Systems
Abstract This paper provides the necessary and sufficient conditions for a multi-degrees-of-freedom linear potential system with an arbitrary damping matrix to be uncoupled into independent subsystems of at most two degrees-of-freedom using a real orthogonal transformation. The incorporation of additional information about the matrices, which many structural and mechanical systems commonly possess, shows a reduction in the number of these conditions to three. Several new results are...
Download 2024 Ranislav M. Bulatovic , Firdaus E. Udwadia
ASME International
Decomposition and Uncoupling of Multi-Degree-of-Freedom Gyroscopic Conservative Systems
Abstract This paper explores the decomposition of linear, multi-degree-of-freedom, conservative gyroscopic dynamical systems into uncoupled subsystems through the use of real congruences. Two conditions, both of which are necessary and sufficient, are provided for the existence of a real linear coordinate transformation that uncouples the dynamical system into independent canonical subsystems, each subsystem having no more than two-degrees-of-freedom. New insights and conceptual simplifications...
Download 2023 Ranislav M. Bulatovic , Firdaus E. Udwadia
ASME International
Uncoupling of Linear Multi-Degree-of-Freedom Damped Gyroscopic Potential Systems
Abstract This paper deals with the uncoupling of linear damped multi-degree-of-freedom gyroscopic potential systems in which the damping is taken to have a specifically chosen form. Necessary and sufficient conditions are obtained that guarantee the uncoupling of such damped systems into independent subsystems with at most two degrees-of-freedom. Along with several other results, it is shown that when the potential (stiffness) matrix of the damped system has distinct eigenvalues—a...
Download 2023 Ranislav M. Bulatovic , Firdaus E. Udwadia
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Copyright © 2026 EmpowerHR4Inno. All right reserved.
Copyright © 2026 EmpowerHR4Inno. All rights reserved.