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-to-charge ratio used as its unit in the field of mass spectrometry. Some fields use the charge-to-mass ratio ("Q"/"m") instead, which is the multiplicative inverse of the mass-to-charge ratio. The 2014 CODATA recommended value for an electron is = . When charged particles move in electric and magnetic fields the following two laws apply: where F is the force applied to the ion, "m" is the mass of the particle, a is the acceleration, "Q" is the electric charge, E is the electric field, and v × B is the cross product of the ion's velocity and the magnetic flux density. This