https://doi.org/10.1140/epjp/s13360-023-04676-w
Regular Article
Integrals of motion for a translating and draining, S-shaped pipe
Department of Aerospace Engineering, College of Engineering, Texas A&M University, 77843-3141, College Station, TX, USA
Received:
5
October
2023
Accepted:
9
November
2023
Published online:
28
November
2023
A comprehensive study of the dynamic behavior of a translating, fluid-draining, S-shaped pipe is presented. The equations of motion are rigorously developed using a version of Lagrange’s equations that befits variable-mass systems. The equations are then analytically integrated to reveal integrals of motion that offer insights into the system’s behavior. This problem and solution is accessible to students and teachers, providing practice with mathematical modeling, differential and integral calculus, momentum balance, and phase space portraits.
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© The Author(s), under exclusive licence to Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature 2023. Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
