ABSTRACT
This chapter discusses the literature on the Trojan “swarms” and focuses on the dynamics of the Jupiter Trojans. It introduces the theory of the restricted three-body problem (RTBP), which is the basis of understanding the motion of the asteroids. The classical RTBP consists of the following restrictions with respect to the general three-body problem: the third body is thought to be massless and thus is not affecting the Keplerian motion of the two primaries (masses m1 and m2), the motion of the third body takes place in the plane of motion of the two primaries, and the motion of the primaries is circular. The chapter discusses the importance of the types of resonances within the 1:1 mean motion resonance with Jupiter. The types include the secular resonances, the Kozai resonance and the three-body mean motion resonance. The chapter provides some examples of peculiar orbits in connection with the complicated dynamics of asteroids in stable chaotic motion.
