Lagrangians for classically damped linear multi-degrees-of-freedom dynamical systems are obtained using simple and elementary methods. Such dynamical systems are very widely used to model and analyze small amplitude vibrations in numerous naturally occurring and engineered systems. An invariant of the motion is also obtained.
Inverse Problem of Lagrangian Mechanics for Classically Damped Linear Multi-Degrees-of-Freedom Systems
Contributed by the Applied Mechanics Division of ASME for publication in the JOURNAL OF APPLIED MECHANICS. Manuscript received February 1, 2016; final manuscript received June 22, 2016; published online July 25, 2016. Assoc. Editor: Alexander F. Vakakis.
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Udwadia, F. E. (July 25, 2016). "Inverse Problem of Lagrangian Mechanics for Classically Damped Linear Multi-Degrees-of-Freedom Systems." ASME. J. Appl. Mech. October 2016; 83(10): 104501. https://doi.org/10.1115/1.4034012
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