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Mechanical oscillators described by a system of differential-algebraic equations. (English) Zbl 1249.34017

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.

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
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