Dynamics of a particle with damping, friction, and percussional effects
The authors discuss and solve a mathematical model for the dynamics of a particle moving in a line and subjected to friction and percussional effects. The interaction between physical meaning and mathematical approach are illustrated in details. The model consists of a second order ordinary differential equation (the equation of dynamics) and an inclusion (Coulomb's friction law) [see also \textit{J. J. Moreau}, Trends in Applications of Pure Mathematics to Mechanics, Vol. 2, Collect. pap. present. Symp. Kozubnik/Poland 1977, 263-280 (1979; Zbl 0433.73096)]. The differential equation is considered in weak sense, more precisely, the solution is a function whose first derivative is a function of bounded variation and the second derivative is a measure. The authors adopt a successive approximation process which consists in associating to the main problem (P) a sequence of problems \((P_n)_n\) with a finite number of percussions. For related results see also \textit{J. J. Moreau} [Topics in Nonsmooth Mechanics, 1-74 (1988; Zbl 0657.28008) and \textit{M. D. P. Monteiro Marques} [Differential inclusion and nonsmooth mechanical problems. Shock and dry friction, Basel (1993; Zbl 0802.73003)].
scientific article; zbMATH DE number 861858