By Donald Greenspan
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34, and P0/ - P0/ the third row. 57), let G Ξ H Ξ m Ξ 1, 24 34 l p = 7, q = 10. 5) while so that P 13 the remaining particles are centered at the vertices of the hexagons. 4), one of relative configuration stability. The motion of the particles will be completely determined once we fix the initial To do this, let us suppose that the particles and v. Λ velocities v. n i,0,x i,0,y have just been emitted horizontally from a nozzle. If this were the case, then v. Λ would dominate v. Λ . Moreover, not all particles would have exactly i,0,x 1,0,y the same velocities because of possible collisions with the nozzle housing, and so forth.
K+l q-1 ξ=0 q-1 ( ij,krij,k+lVrij,k+l i = 1 , 2 , . ,N. 57) REMARK Only for simple forces, like gravity, do the continuous and the arithmetic ap proaches yield exactly the same dynamical behavior. In general (, ), the 3 two approaches yield results which differ by terms of order (At) in both posi tion and velocity. Recently , new numerical formulas have been developed which increase this order of magnitude difference to any prescribed exponent, but, for these, the conservation of angular momentum of systems which have more than one particle is still to be proved.
6. 7). Heat will'be transferred to the body by increasing the velocity, and hence the kinetic energy, of various body particles as follows. At each time step of particle Pi to the heat source. If Ri 1. 5, tk, consider the distance Ri then P ' s velocity is left unchanged. 37) so that the intensity varies as an inverse square, with r being a positive variation constant, and along the line joining the center of the particle and the center of the heat source. In order to simulate a gradual increase of heat at the .