TABLE OF CONTENTS In this chapter, we examine systems of rigid bodies. Our goal is simply to discover how our previous developments can be used to obtain the equations of motion for these systems. As you might imagine, the equations of motion can be very complex, and judicious component selections from the balance laws are often needed to extract the equations of motion. This is illustrated with the example of a rate gyroscope.
The presentations here are limited in scope and we do not have the opportunity to discuss many interesting systems featuring several rigid bodies such as the dualspin spacecraft, bicycles, gyrocompasses, and the Dynabee in detail. As discussed in [86], a dual-spin satellite has the ability to reorient itself in an environment where the resultant moment on the satellite is negligible. This ability has been used in communications satellites and was employed in the Galileo spacecraft. This spacecraft was launched in 1989 and some 6 years later began its orbits of the planet Jupiter. These orbits were designed so that the spacecraft could capture data on some of the largest moons of Jupiter; Galileo s mission was a remarkable success. [*] The Dynabee (or Rollerball) was invented in the early 1970s by Archie Mishler [141] and features spinning a rotor to speeds in excess of 5000 rpm by carefully rotating an outer casing (housing). This novel gyroscopic device is discussed in an exercise at the end of this chapter.
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