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Nonsmooth Mechanics - Models, Dynamics and Control (Paperback, 2nd ed. 1999. Softcover reprint of the original 2nd ed. 1999)
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Nonsmooth Mechanics - Models, Dynamics and Control (Paperback, 2nd ed. 1999. Softcover reprint of the original 2nd ed. 1999)
Series: Communications and Control Engineering
Expected to ship within 10 - 15 working days
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Thank you for opening the second edition of this monograph, which
is devoted to the study of a class of nonsmooth dynamical systems
of the general form: :: i; = g(x, u) (0. 1) f(x, t) 2: 0 where x E
JRn is the system's state vector, u E JRm is the vector of inputs,
and the function f (-, . ) represents a unilateral constraint that
is imposed on the state. More precisely, we shall restrict
ourselves to a subclass of such systems, namely mechanical systems
subject to unilateral constraints on the position, whose dynamical
equations may be in a first instance written as: ii= g(q, q, u) (0.
2) f(q, t) 2: 0 where q E JRn is the vector of generalized
coordinates of the system and u is an in put (or controller) that
generally involves a state feedback loop, i. e. u= u(q, q, t, z),
with z= Z(z, q, q, t) when the controller is a dynamic state
feedback. Mechanical systems composed of rigid bodies interacting
fall into this subclass. A general prop erty of systems as in (0.
1) and (0. 2) is that their solutions are nonsmooth (with respect
to time): Nonsmoothness arises primarily from the occurence of
impacts (or collisions, or percussions) in the dynamical behaviour,
when the trajectories attain the surface f(x, t) = O. They are
necessary to keep the trajectories within the subspace " = {x: f(x,
t) 2: O} of the system's state space."
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