Projected dynamical system: Difference between revisions

Revision as of 16:47, 1 July 2006

Revision as of 15:45, 7 July 2006

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</math>

On the [[interior]] of ''K'' solutions behave as they would if the system were an unconstrained ordinary differential equation. However, since the vector field is discontinuous along the boundary of the set, projected differential equations belong to the class of discontinuous ordinary differential equations. While this makes much of ordinary differential equation theory inapplicable, it is known that when ''-F'' is a [[Lipschitz]] continuous vector field, a unique [[absolutely continuous]] solutionssolution exists through each initial point ''x(0)=x₀'' in exist''K'' on the interval <math>[0,\infty)</math>.

This differential equation can be alternately characterized by