strap-on booster
Strap-on boosters are rocket motors that are mounted around the first stage of a launch vehicle to provide extra thrust at lift-off and during the first few minutes of ascent. Most strap-ons, as in the case of the Space Shuttle, Titan, Delta, Atlas, and Ariane, are solid-propellant motors. Some Russian launch vehicles have used liquid-propellant engines. Typically, strap-on boosters burn out while the first stage is still firing, separate, and fall back to Earth. For this reason, they are sometimes referred as a half stage or zero stage.