Multiple Nonlinear Lumped Systems (Institute of Fundamental Technical Research, Polish Academy of Sciences, Applied Mechanics Series)

Oversized cloth hardcover, 332 pages, NOT ex-library. Limited academic edition of 390 copies. A touch of spotting to endpapers. Pages are in nice shape, clean, untanned, with unmarked text, free of inscriptions and stamps. Rear upper hinge gently cracked, binding remains firm and secure throughout. A foreign price stamp on the rear board. No dust jacket. -- A highly technical mathematical monograph in the field of nonlinear mechanics and control theory. It focuses on the qualitative analysis and stability of complex mechanical or electrical systems that are "lumped" (represented by a finite number of variables rather than continuous fields). Analytical Scope and Content: - The work is centered on the structural behavior of systems with multiple degrees of freedom. Rather than focusing on simple linear approximations, Skowronski provides rigorous methods for handling the complexities of real-world nonlinearities: - Qualitative Analysis: The book emphasizes the global behavior of systems - investigating where they are stable, where they oscillate, and how they react to external perturbations. - The Delta Method: The text utilizes specialized grapho-analytical methods to solve ordinary differential equations in phase space. - Energy and Liapunov Functions: Skowronski employs energy-based approaches and Liapunov's second method to determine the "boundedness" and stability of the system's trajectories without requiring exact solutions to the equations. - Engineering Applications: While mathematically rigorous, the text is aimed at solving problems in mechanical engineering, robotics, and electrical circuit theory where nonlinear damping or spring characteristics are present.