## Arithmetic applied mathematics |

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4-vector acceleration angular momentum arithmetic assume CALCULATE CALL COPVAR Chapter computations concepts conservation consider CONTINUE coordinates determined develop distance dynamical equation example flow follows formulas given gravity Greenspan harmonic oscillator heat ij,k ij,k+l ij,k+l imply initial data initial positions INITIAL VELOCITY invariant ITERATION k+l k kinetic energy lab frame let particle linear momentum liquid Lorentz invariant Lorentz transformation magnitude mathematical Minkowski space motion N-body N-body problem Newton's method Newtonian mechanics numerical OOOO OOOOOOOOO parameter choices particle Pi physical Pi at tk relativistic mechanics respectively rest mass rocket frame Section short range forces shown in Fig solid particles special relativity speed Stefan problem SUBROUTINE Table three particles three-body problem TIMESTEP triangular building blocks vector vi,k vk+l vk+l,y x y vx vy xi,k xk+l yields