This textbook on models and modeling in mechanics introduces a new unifying approach to applied mechanics: through the concept of the open scheme, a step-by-step approach to modeling evolves. The unifying approach enables a very large scope on relatively few pages: the book treats theories of mass points and rigid bodies, continuum models of solids and fluids, as well as traditional engineering mechanics of beams, cables, pipe flow and wave propagation.
From the reviews: "Mathematical modeling is usually described as an art rather than a science. Models of Mechanics, by Anders Klarbring, shows that there is indeed a science of mathematical modeling. While the book is obviously focused on developing models specifically for mechanics, it has a broader value as a general exposition of mathematical modeling. For this reason, this small book belongs on the bookshelves of mathematical modelers who do not work in mechanics, as well as those that do." (Glenn Ledder, SIAM Review, Vol. 49 (3), 2007) "Klarbring's book is a clear and concise introduction into the foundations of classical mechanics for discrete particles, fluids, and solids ... . It is aimed at the intermediate level ... seasoned researchers will appreciate the philosophically unified approach to the various systems that are considered. ... the text succeeds in providing a unified approach to the modeling of mechanical processes for a broad class of materials and systems." (Thomas Pence, Meccanica, Vol. 44, 2009)
Innehållsförteckning
General Background.- Open scheme.- Basic Models: Geometry and Universal Laws.- Bodies and Their Placements in ?.- Discrete Model.- One-Dimensional Model.- Pipe Flow.- Three-Dimensional Model.- Complete Models by Adding Particular Laws.- Particular Laws.- Small Displacement Models.- Pipe Flow Models.- Models of Fluid Mechanics.- Kinematic Constraints, Beams and Rigid Bodies.
