Download Bifurcation and Chaos in Nonsmooth Mechanical Systems (World by J. Awrejcewicz, Claude-Henri Lamarque PDF

By J. Awrejcewicz, Claude-Henri Lamarque

This quantity offers the theoretical body for learning lumped nonsmooth dynamical platforms: the mathematical tools are recalled, and tailored numerical equipment are brought (differential inclusions, maximal monotone operators, Filippov concept, Aizerman theory). instruments on hand for the research of classical tender nonlinear dynamics (stability research, the Melnikov procedure, bifurcation eventualities, numerical integrators, solvers) are prolonged to the nonsmooth body. Many types and purposes bobbing up from mechanical engineering, electric circuits, fabric habit and civil engineering are investigated to demonstrate theoretical and computational advancements.

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Read or Download Bifurcation and Chaos in Nonsmooth Mechanical Systems (World Scientific Series on Nonlinear Science: Series A) (v. 45) PDF

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Additional info for Bifurcation and Chaos in Nonsmooth Mechanical Systems (World Scientific Series on Nonlinear Science: Series A) (v. 45)

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Domain HI Fig. 7 Domain I ** Domain II I Phase portrait of the investigated system with the marked switching lines. However, a key attention should be focused on determination of the jumps between different families of solutions which occur on the switching which depend on the velocities w. 36) where U(T+) and u(r~) correspond to the right- and left- hand side limits of the function u{t] in the point r. Note that in case of continuity at point T we have Au(r) — 0. A similar definition holds for the derivatives and integrals.

84) and initial condition £0 that is a given random variable defined on (Q, F, P). Under previous assumptions, [Kree (1982)] or [Cepa (1995a)] prove some existence and uniqueness results by using rather sophisticated mathematical frame and methods (see in the quoted references for details). They provide a correct mathematical sense to the words "solution", "existence" (weak and strong existence of solutions) and "uniqueness" (in a probability sense). We do not intend to go inside further mathematical developments.

51) dM(x) = Md(j>(x). 53) (2-53) [ || G(t,Xx) - G{t,X2) ||< W G || X! c. function on W. Such a frame is easily obtain from fundamental relation of dynamics and M is then derived from mass matrix. 7 V£ G D(d),3\X € W^fato + T ] , R P ) SO that { for almost every t G [t0, t0 + T},X(t) + Md

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