A theory of systems with unilateral constraints

Penalty Approximation for Non-smooth Constraints in Vibroimpact

“…If we choose p small enough for 12pEδ/(1 − p) 5 to be less than or equal to 1/2, it is clear that we can choose k 0 large enough for the sum of the remaining terms in (3.67) to be less than or equal to 1/4.…”

“…Mathematical results relative to the convergence of a penalty approximation of impact problems have been obtained by several authors when the energy is conserved; see for instance [13], [14], and also [3], [1] [2], [12], [6], [8], [7], [5], [4] and [10].…”

On the dynamics of systems with one-sided non-integrable constraints

“…As it became known after a classical work by Caratheodory, the motion of a free system under the action of a viscous friction tends to the motion with a twosided differential constraint as we infinitely increase the coefficient of the viscous friction [5]. A similar idea has been considered in the theory of holonomic systems with one-sided constraints: the 'forbidden' region of the configuration space is filled by the visco-elastic Kelvin-Foight continuum, then a limit passage, for which the coefficients of viscosity and elasticity are increased in a consistent manner, is applied.…”

The necessary conditions for the stability of steady motions of systems with constraints produced by large potential forces

“…We will assume that an additional force with a potential (compared with [6,5]) (1.2) which depends on the positive parameter N, also acts on the system, where respectively. We will assume thatf(x) is a continuous function in R n, and the smooth surface % can be split into n-dimensional regions %_ and % +.…”