Ebook: Local stereology

This text presents the methods of analysis of dynamical mechanical systems subjected to stochastic excitations in form of random trains of impulses. This particular class of excitations is adequately characterized by stochastic point processes and behaviour of dynamical systems is governed by stochastic differential equations driven by point processes. Based on the methods of point processes, the analytical techniques are devised to characterize the response of linear and nonlinear mechanical systems as the solutions of underlying stochastic differential equations. A number of example problems of engineering importance are also solved, such as the vibration of plates and shells, and of nonlinear oscillators under random impulses 1. Introduction to stereology -- 2. The coarea formula -- 3. Rotation invariant measures on [actual symbol not reproducible] -- 4. The classical Blaschke-Petkantschin formula -- 5. The generalized Blaschke-Petkantschin formula -- 6. Local slice formulae -- 7. Design and implementation of local stereological experiments -- 8. The model-based approach -- 9. Perspectives and future trends -- App. Invariant measure theory