By Jan Awrejcewicz (auth.)
This is the 1st quantity of 3, dedicated to Mechanics. This publication includes classical mechanics difficulties together with kinematics and statics. it is suggested as a supplementary textbook for undergraduate and graduate scholars from mechanical and civil engineering, in addition to for actual scientists and engineers. It incorporates a uncomplicated creation to classical mechanics, together with basic rules, statics, and the geometry of lots, in addition to thorough dialogue on kinematics.
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Extra info for Classical mechanics: kinematics and statics
In what follows we apply the statements and comments introduced thus far. Let us emphasize that the net result of a couple relies on the production of a moment M (couple vector). Since M is independent of the point about which it takes place (free vector), then in practice it should be computed about a most convenient point for analysis. One may add two or more couples in a geometric way. One may also replace a force with (a) an equivalent force couple at a specified point; (b) a single equivalent force provided that F ?
Let us now return to Fig. 2, where the system of concurrent forces acts solely on the rigid body. 11), in view of the fact that the number of unknowns should not exceed three (or, in the case of the planar system of forces, two) for the considered force system to be statically determinate. In Fig. 5 a symmetrical system of concurrent forces formed after suspending the body of weight G from three ropes is shown. 1 A Concept of Equilibrium 29 Fig. 5 A weight G suspended from three (four) ropes in space (a) and a system of concurrent forces (b) from three equations and, consequently, describe the forces F1 , F2 , and F3 .
The six mutually independent axes should be taken in such a way as to formulate six independent equations only. 29) consisting of six equations resulted from projecting the main force vector S, and the main moment of force vector MO reduced to an arbitrary point O (Sect. 3), where the point of reduction O is the origin of the Cartesian coordinate system. The state of equilibrium of the considered rigid body means that it does not make any displacement, that is, neither translation nor rotation about point O and consequently with respect to the adopted coordinate system OX1 X2 X3 .