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There is given the complete exposition of a mathematical formalism and the working tools of mechanics of multibody systems based on methodology of the system analysis. Essentially in a new fashion the problem of designing of the differential equations of constraints of a general kind of multibody systems with environment bodies is represented. Two algorithms of direct analytical designing of a reverse matrix of kinetic energy of system are developed, passing stages of designing of the matrix and its subsequent reversing. The created algorithms are most numerically economic among known....

This book is unique in its emphasis on developing fundamentals of Galilean mechanics, under the conditions rejecting discreteness of 'analytic' mechanics, rejecting presence of rotating and deformation particles in locally continuous media. The main properties of Galilean mechanics universe are formulated as axioms of density balance for 6-- dimensional bi-vector measures (screws). This leads to the principally new architecture of Galilean mechanics as geometry of generalized Galilean group. Audience: graduate students and researchers in the field of mathematics and mechanics.