We consider a linear system of differential equations with pulse action and establish a condition for the construction of its mechanical analogs.
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A. M. Samoilenko and N. A. Perestyuk, Impulsive Differential Equations [in Russian], Vyshcha Shkola, Kiev (1987); English translation: World Scientific, Singapore (1995).
Ya. Z. Tsypkin, Theory of Linear Impulsive Systems [in Russian], Fizmatgiz, Moscow (1958).
A. A. Martynyuk, J. N. Shen, and I. P. Stavroulakis, “Stability theorems in impulsive equations with infinite delay,” in: A. A. Martynyuk (editor), Advances in Stability Theory at the End of the 20th Century, Taylor and Francis, London–New York (2003), pp. 153–175.
V. B. Larin, Control of Walking Machines [in Russian], Naukova Dumka, Kiev (1980).
V. B. Larin, “A note on a walking machine model,” Prikl. Mekh., 39, No. 4, 122–132 (2003).
V. I. Slyn’ko, “Linear matrix inequalities and stability of motion of impulsive systems,” Dopov. Nats. Akad. Nauk Ukr., No. 4, 68–71 (2008).
V. S. Denisenko and V. I. Slyn’ko, “Impulsive stabilization of mechanical systems in Takagi–Sugeno models,” Prikl. Mekh., 45, No. 10, 115–130 (2009).
V. V. Novyts’kyi and L. V. Petryshyna, “Decomposition and mechanical analogs. I. Linear stationary systems,” in: Problems of Analytical Mechanics and Its Applications, Institute of Mathematics, Ukrainian National Academy of Sciences, Kyiv (1999), pp. 251–256.
H. Goldstein, Classical Mechanics, Addison-Wesley, Reading, MA (1980).
F. R. Gantmakher, The Theory of Matrices [in Russian], Nauka, Moscow (1967).
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Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 63, No. 1, pp. 140–144, January, 2011.
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Pryz, A.M. Mechanical analogs of linear impulsive systems. Ukr Math J 63, 169–176 (2011). https://doi.org/10.1007/s11253-011-0495-y
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DOI: https://doi.org/10.1007/s11253-011-0495-y