With the basis from Chapter 2, we are now able to take a closer look at the motion of galaxies, i.e. their trajectories. A powerful tool in the study of interactions between galaxies in the nonlinear regime is the AVP, which will be the subject of this chapter. Section 3.1 will deal with the approximations that the AVP is based on, Section 3.2 will present Hamilton's principle from mechanics, and in Section 3.3, the equations of motion for galaxies in an expanding universe will be deduced.