This updated and enriched new edition maintains its complementarity principle in which the subgroup of rotations, harmonic oscillators, and the conventional complex analysis generate linear and weakly nonlinear approaches, whereas translations and reflections, impact oscillators, and hyperbolic Clifford's algebras, give rise to the essentially nonlinear "quasi-impact" methodology based on the idea of non-smooth temporal substitutions. In the years since "Nonlinear Dynamics: Between Linear and Impact Limits," the previous edition of this book, was published, due to a widening area of applications, a deeper insight into the matter has emerged leading to the rudimentary algebraic view on the very existence of the complementary smooth and non-smooth base systems as those associated with two different signs of the algebraic equation j2 =± 1. This edition further includes an overview of applications found in the literature after the publication of first edition, and new physical examples illustrating both theoretical statements and constructive analytical tools.

• Presents an improved picture of non-smooth temporal transformations using impact systems as a basis for various analyses;
• Includes new examples of recent applications for problems in energy absorption/harvesting and resonance interactions;

• Describes a complementarity principle with a range of applications from smooth to discontinuous oscillatory processes.

  Autorentext

  Dr. Valery N. Pilipchuk is Associate professor of Mechanical Engineering at Wayne State University, Detroit, Michigan, USA.