Three-body encounters in a stellar system can result in the formation of a binary system if the third star carries away sufficient kinetic energy to leave the other two bound. Subsequent encounters with such a binary are one of the main mechanisms for dynamical evolution of the system. In chapter two the energy change in a hard binary is calculated when the third star moves on a distant nearly parabolic orbit. Previous results fail in certain important cases (e.g. a circular binary), and the new results give a complete treatment. Chapters three and four are motivated by the problem of determining the rate at which stars escape from a globular cluster. This process has important consequences for the evolution of systems of globular star clusters. Hénon(1988) developed a model problem which mimics chaotic aspects of a star's motion within a globular cluster. This model (chapter three) describe a particle bouncing on an inclined surface and is used to understand the mechanism underpinning the escape process in globular clusters. Orbital trajectories of escaping stars are investigated in chapter four by applying parts of the theory presented in chapter three. The motion of a star within a globular cluster is modelled using Hill's Equations. By applying numerical integration the trajectory of a star, with given initial conditions, may be followed in phase space. Different cases are considered depending on whether the cluster moves in a circular or noncircular orbit around the centre of the galaxy. In the circular case the orbital motion is viewed on an appropriate surface of section. Escaping stars are all found to lie inside a tubular surface which connects the cluster with the outside world. In the noncircular case the initial conditions leading to stable/unstable orbits are investigated. The escape process for highly eccentric orbits is modelled by supposing that the star is subjected to an impulsive force each time the cluster moves through the galactic pericentre.