N-body problem of first-order differential equations, with initial conditions as initial position coordinates and initial momentum values. Symmetries in the -body problem yield global integrals of motion that simplify the problem. Translational symmetry of the problem results in the center of mass moving with constant velocity, so that , where is the linear velocity and is the initial position. The constants of motion and represent six integrals of the motion. Rotational symmetry results in the total angular momentum being constant where × is the cross product. The three components of the total angular momentum yield three more constants of the motion. The
Mass driver then use the mass driver to accelerate pieces of matter of almost any sort, boosting itself in the opposite direction. At the smallest scale of reaction mass, this type of drive is called an ion drive. No absolute theoretical limit is known for the size, acceleration or muzzle energy of linear motors. However, practical engineering constraints apply for such as the power-to-mass ratio, waste heat dissipation, and the energy intake able to be supplied and handled. Exhaust velocity is best neither too low nor too high. There is a mission-dependent limited optimal exhaust velocity and specific impulse for any thruster