Download Examples to Extremum and Variational Principles in by Dieter Besdo (auth.) PDF
By Dieter Besdo (auth.)
Read or Download Examples to Extremum and Variational Principles in Mechanics: Course Held at the Department of General Mechanics October 1970 PDF
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Additional resources for Examples to Extremum and Variational Principles in Mechanics: Course Held at the Department of General Mechanics October 1970
Sample text
The second equation of motion is eq. (4). Equation (6) is the only relation which contains A- 2 , which, therefore, can be calculated by eq. {6), but this equation is of no interest if we want to calculate the equations of motion. Rearranging the result we get 41 LAGRANGE Eqs. of 1st Kind/D'ALEMBERT's Principle b) D'ALEMBERT's principle Formula : a'w = .. ~ ( p. - m. ) <>'x· = ~ ~ The relations between the o a·~t can be found when dif- ferentiating c:p k with respect to the coordinates. From Table PJ, m•, X• , so we can state : 2.
2. 2-2 .. a) D 38 2. Virtual Work Principles Fig. 2. 2-2b) Fig. 2. 2-2 c) We see from Fig. 2. 2 that the possibly interesting forces can be described by the coordinates printed in Fig. 2. 22c. ~ has to be chosen in such a way that K = 0 if X= \i. - x). We have introduced four coordinates, but the system has only two degrees of freedom, so we must add two constraints ( 1) (2)
These coordinates are free, but the direction of the velocity '\1 P of point 48 2. Virtual Work Principles y '---v---' X effective X X inertia force coordinates forces ~,'I'}: auxiliary coordinates Fig. 2. 3-2 P is restricted (underlining denotes physical vectors) : is parallel to the ~-axis. ) p V 'P v 'rl = 0. ~ Thus, we have the constraint : - x ~~n "i' + ~ co~ " - "" t = 'P '\T 11 =0 . (1) This inholonomic constraint allowes the calculation of the quantities