The metal-case is "ground earth" only if its physially connected to earth ground. For example, in typical consumer electronics (with metal cases), the metal case would be at earth ground when the unit is plugged into the wall by virtue of the grounding prong on the plug.
i ask two questions;first is antenna "ground" metal-case,or no;the second is "metal-case" "gound" earth,or no;Battery-powered equipment;usually is used for outdoor;thanks!