  An investigation into the properties of a two dimensional (2D+1) system of
self propelled particles (known as boids) in free space is conducted using a
Lagrangian Individual-Based Model. A potential, associated with each boid is
specified and a Lagrangian is subsequently derived in order to obtain the
equations of motion for each particle in the flock. The Morse potential and the
Lennard-Jones potential, both well understood in atomic and molecular physics,
are specified. In contrast to the original model proposed by Vicsek [Phys. Rev.
Lett. 75, 1226 (1995)] systems are considered with open boundary conditions.
These two models successfully replicate the phases observed in Vicsek's
original model, as well as several other significant phases, providing a
realistic model of a wide range of flocking phenomena.
