This is a device called a "Pendulous Integrating Gyroscope" and is a common part of guidance systems used in many spacecraft and missiles, for a variety of civil and military customers. It contains a gyroscope, floated in a viscous fluid and kept at a constant temperature. A small weight mounted off the center of mass acts as a pendulum, and measures acceleration to a high accuracy. It also mathematically integrates that measurement of acceleration over time, giving velocity.
This particular artifact was used in tests and was not flown. It was designed by the Charles Stark Draper Laboratory in Cambridge, Massachusetts, and manufactured by the AC Sparkplug Division of General Motors in Milwaukee, Wisconsin.
This object is on display in Rockets & Missiles at the Steven F. Udvar-Hazy Center in Chantilly, VA.