By Jan Awrejcewicz (auth.)
This is the 1st quantity of 3, dedicated to Mechanics. This e-book includes classical mechanics difficulties together with kinematics and statics. it is strongly recommended 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 simple creation to classical mechanics, together with primary ideas, statics, and the geometry of plenty, in addition to thorough dialogue on kinematics.
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Additional info for Classical mechanics: kinematics and statics
16 Space force system F1 ; : : : ; FN acting on a rigid body (a) and its reduction to a pole O (b) shown. The latter boils down to applying at point O all the vectors of forces F1 ; : : : ; FN and moments M1 ; : : : ; MN determined in a way that is analogous to that shown for the case of force F1 . The application of Poinsot’s method led to obtaining the concurrent force and moment system, which is schematically depicted in Fig. 16b. 24) nD1 The technique described above is equivalent to the theorem on parallel translation of force.
13 Closed funicular polygon (M D 0) 2. If the funicular polygon is not closed but the force polygon is closed, then planar force system is equivalent to a moment of force (couple). 3. If both force and funicular polygons are closed, then the force system is equivalent to zero. The final geometrical equilibrium condition for a two-dimensional force system reads: A planar force system is equivalent to zero if both the force polygon and funicular polygon are closed. 1. Three vertical forces F1 , F2 , F3 act on a horizontal beam of length l depicted in Fig.
The bodies are in translatory motion. Determine the accelerations of the bodies. Let us associate the virtual displacements ıx1 , ıx2 , and ıx3 with the respective coordinates. Fen mn an / ı ırn D 0: i Dn In the present case the weights of the bodies play the role of external forces F1 D m1 g; F2 D m2 g; F3 D m3 g; and, moreover, ırn D ıxn En , n D 1; 2; 3. 4 Increment of a Function and Variation of a Function 19 Fig. 4 Three bodies of masses mi , i D 1; 2; 3 in translatory motion m3x3 x3 x2 m3g x1 m2x2 m1x1 m2g m1g Let us assume that the coordinates x1 and x3 are independent.