By Ying, Shuh-Jing (Benjamin)
The publication balances conception and alertness and relates all matters to sensible difficulties, real-world occasions, and up to date advances that have an effect on lifestyle. this article distinguishes itself with a extra whole creation to fresh advancements in dynamics, new and functional purposes to assist the reader take note key theories and makes use of, and an appreciation that the subject material is riddled with ongoing difficulties that want new solutions.
- information and knowledge showing during this e-book are for informational reasons simply. AIAA and the writer should not answerable for any harm or harm caused by use or reliance, nor do AIAA and the writer warrant that use or reliance should be loose from privately owned rights.
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0 F2 = 16000. LT. 00005 A M = 5 6 4 . 03138596 A Z 0 = Z 1 0 + Z 1 ( N ) * 0 . 03138596 AX1 = X 1 0 - X I ( N + I ) 0 . 9 9 9 5 0 7 3 4 + Z I ( N + l ) 0 . GT. LT. GT. LT. 03138596)/1000. 03138596)/1000. x1(1) = x x X2(I) = X2(I)/1000. Z2(I) = Z2(I)/1000. 4,'m') 25 FORMAT ('MAXIMUM ITERATIONS EXCEEDED') 250 STOP END SUBROUTINE RK (X,Z,VXN,VZN,AH,AM,DM,EG) AK1 = AH*(F/AM)*VXN/SQRT(VXN**2+VZN**2) BK 1 = A n * ((F/AM)* VZN/SQRT(VXN**2+VZN** 2)-G) XK1 = AH*VXN ZK1 = AH*VZN AM = AM-DM*AH/2. ) AM = AM-DM*AH/2.
42 ADVANCED DYNAMICS Fig. 9 Point P located outside a uniform solid sphere. Solution. 1) Outside a uniform solid sphere, consider that a particle with unit mass is located at P; the distance between the center of the sphere and the particle is r as shown in Fig. 9. The infinitesimal volume under consideration is dv = (2zrr '2 sinO)dOdr' The distance between p and dv is L = ~ / r 2 + r '2 -- 2rr'cosO Using Eq. 34) r where M is the mass of the solid sphere. This result states that the potential of unit mass outside a solid sphere is equivalent to that of a point mass with the same mass concentrated at the center of the sphere.
Hence there are three equations, but, in general, there are four unknowns: Vl'x, V;y, V~'x, V~y, the velocity components after the collision. To determine them, additional conditions must be specified. In the collision process, no coordinate system exists in the space. Without loss of generality, we choose x axis along the line of impact and y axis along the plane of impact. , V~y = Vly V~y = V2y Then the momentum and energy equations become ml Via. 40) ml Vl2x + m2 V2~. 41) Now V[x and V~x can be determined by Eqs.
Advanced Dynamics by Ying, Shuh-Jing (Benjamin)