# On differential systems with quadratic impulses and their applications to Lagrangian mechanics

@inproceedings{Bressan1993OnDS,
title={On differential systems with quadratic impulses and their applications to Lagrangian mechanics},
author={Alberto Bressan and Franco Rampazzo},
year={1993}
}
This paper is concerned with the basic dynamics and a class of variational problems for control systems of the form $({\text{E}})\qquad \dot x = f(t,x,u) + g(t,x,u)\dot u + h(t,x,u)\dot u^2$ These systems have impulsive character, due to the presence of the time derivative $\dot u$ of the control. It is shown that trajectories can be well defined when the controls u are limits (in a suitable weak sense) of sequences $(u_n )$ contained in the Sobolev space $W^{1,2}$. Roughly speaking, one… CONTINUE READING

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