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home page The ebook balances concept and alertness and relates all matters to functional difficulties, real-world occasions, and up to date advances that impact lifestyle. this article distinguishes itself with a extra entire creation to contemporary advancements in dynamics, new and sensible purposes to assist the reader have in mind key theories and makes use of, and an appreciation that the subject material is riddled with ongoing difficulties that desire new solutions.
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If there are two point masses placed side by side, an attractive force will exist between them. 67 × 10 -11 N-m2/kg 2, and r is the distance between the two point masses ml and m2. "2 as shown in Fig. 7. Then the force acting on m l is mlm2 Fl = G Ir2 - - - - - -rl5 I (r2 - rl) When m2 is a distributed mass, however, the gravitational force on m l becomes FI =ml p(r') d r ' . G~:~(r--r) DYNAMICS OF A SYSTEM OF PARTICLES 41 n~ 1 ~ Fig. 3 . 7 Relationship F ~W i l m2 between two point masses. where p (r') is the density of the distributed mass.
2. The example illustrates that as two missile sites are a few hundred kilometers apart, the spherical surface of the Earth must be considered in the determination of the launching angle. Otherwise the second missile will not collide with the first missile if the launching angle is set according to the fiat ground formulation. The gravitational force studied in the missile-to-missile collision is approximated to be always parallel to the z axis. The gravitational force, however, is easily modeled toward the center of Earth with a major component in the k direction and a small component in i direction where i and k are along the Cartesian coordinates chosen at the missile site.
4 Gravitational Force and Potential Energy When a point mass is in the vicinity of a large mass, such as Earth, it experiences a gravitational force directed toward the mass center of the large mass and possesses a potential energy with respect to the large mass. If there are two point masses placed side by side, an attractive force will exist between them. 67 × 10 -11 N-m2/kg 2, and r is the distance between the two point masses ml and m2. "2 as shown in Fig. 7. Then the force acting on m l is mlm2 Fl = G Ir2 - - - - - -rl5 I (r2 - rl) When m2 is a distributed mass, however, the gravitational force on m l becomes FI =ml p(r') d r ' .