from a practical point of view, this means that newton's laws of motion are valid in all inertial systems, which means those at rest or those moving with constant speed relative to one considered at rest. this is the law of inertia: a body at rest continues at rest and a body in motion continues in motion in a straight line unless influenced by an external force. a galilean coordinate system is one where the law of inertia is valid. the laws of mechanics of galileo and newton are valid in a galilean coordinate system. if k is a galilean coordinate system, then every other system k' is a galilean coordinate system if it lies at rest or moves according to the law of inertia relative to k. relative to k', the mechanical laws of galileo and newton are as valid as they are relative to k.