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Watching a documentary on the Viking missions, I noticed the launcher had a small red tank/rocket attached to one of the solid boosters. It struck me as an odd feature/placement, as I thought you'd want your rocket to be balanced as symmetrically as possible. I've also not noticed this on other launchers.

You can just see it on this image - mounted on the right side solid booster:

Titan-Centaur launching Voyager 2

What is it and what is its purpose? Do other launchers use it?

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Thrust vector control on the Titan solid rocket motors was accomplished by fluid injection rather than gimbaling the nozzles. Nitrogen tetroxide oxidizer was injected into ports around the circumference of the nozzle to alter the direction of the exhaust and control the vehicle.

The red tank contained the nitrogen tetroxide propellant used in this thrust vector control method.

(emphasis mine)

THRUST VECTOR CONTROL SYSTEM: The TVC is used to maintain a proper vehicle flight path and orientation during the Stage 0 portion of the mission trajectory via signals from the Core Vehicle guidance computer. The desired flight profile is achieved by exerting side forces on each SRM by injecting a flow of gas, at a specified angle, at a defined velocity and for a calculated time into the SRM gas flow stream through the nozzle. The SRM nozzles are at a fixed angle and do not gimbal.

Reference: globalsecurity.org

Flight control during the Stage 0 phase of flight is provided by a Thrust VectorControl (TVC) system in response to commands from the Titan flight control computer. Nitrogen tetroxide injected into the SRM nozzle through TVC valves deflects the thrust vector to provide control . Pressurized tanks attached to each solid rocket motor supply the thrust vector control fluid. Electrical systems on each SRM provide power for the TVC system.

Reference: NASA TM X-68249

enter image description here enter image description here

Drawings from TITAN IIIE/CENTAUR D-IT SYSTEMS SUMMARY

In regards to your comment about asymmetry of the booster, each SRM had a tank, mounted on opposite sides of the vehicle, so it's not as bad as it looks from that photo.

enter image description here

This thrust vector control method has been used by at least one other launcher, the Indian Space Research Organization's Polar Satellite Launch Vehicle. See Ohsin's answer at this question How does a single SRB control attitude? for more information.

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