Pražák, Dalibor; Rajagopal, Kumbakonam R. Mechanical oscillators described by a system of differential-algebraic equations. (English) Zbl 1249.34017 Appl. Math., Praha 57, No. 2, 129-142 (2012). Summary: We study a system of differential-algebraic equations describing the motion of the mass-spring-dashpot oscillator. Assuming a monotone relationship between the displacement, velocity and the respective forces, we prove global existence and uniqueness of solutions. We also analyze the behavior of some simple particular models. Cited in 3 Documents MSC: 34A09 Implicit ordinary differential equations, differential-algebraic equations 34C15 Nonlinear oscillations and coupled oscillators for ordinary differential equations 34A12 Initial value problems, existence, uniqueness, continuous dependence and continuation of solutions to ordinary differential equations Keywords:differential-algebraic equation; existence of solution; uniqueness of solution; mechanical oscillator × Cite Format Result Cite Review PDF Full Text: DOI EuDML Link References: [1] A.F. Filippov: Klassische Lösungen von Differentialgleichungen mit einer mehrdeutigen rechten Seite (Classical solutions of differential equations with multi-valued right-hand side). SIAM J. Control 5 (1967), 609–621. (In English.) · Zbl 0238.34010 · doi:10.1137/0305040 [2] L. Meirovitch: Elements of Vibration Analysis, 2nd ed. McGraw-Hill, New York, 1986. · Zbl 0359.70039 [3] K.R. Rajagopal: A generalized framework for studying the vibration of lumped parameter systems. Mechanics Research Communications 37 (2010), 463–466. http://www.sciencedirect.com/science/article/pii/S0093641310000728 . · Zbl 1272.74297 · doi:10.1016/j.mechrescom.2010.05.010 [4] W. Rudin: Real and Complex Analysis, 3rd ed. McGraw-Hill, New York, 1987. · Zbl 0925.00005 [5] I. I. Vrabie: Differential Equations. An Introduction to Basic Concepts, Results and Applications. World Scientific Publishing, River Edge, 2004. This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.