A coordinate system consisting of the electric potential U, the magnetic field intensity B, and the modified longitudinal invariant K forms a natural system for the analysis of plasma convection in the magnetosphere. In the absence of parallel electric fields the bounce-averaged drift motion of a particle mirror point follows a straight line trajectory in this representation. The steady state equations of motion for particle mirror points are given by dB/dt=W,dU/dt=-(&mgr;/e) W, and dK/d=O, where W is a generalized velocity function given by W=[(∇U¿∇B) ⋅nK>/(B⋅nK) and nK is a unit vector perpendicular to the local constant K surface. W depends only upon position in the magnetosphere, independent of any particle properties. However, W is proportional to the rate of transformation between potential energy and particle kinetic energy. The surfaces on which W vanishes form natural boundaries betwen accelerator regions (W>0) and dynamo regions (W>0) of the magnetosphere. The occurrence of forbidden zones for particles and the distinction between various types of particle trajectories are determined by the topology of these boundaries and can be easily visualized. The coordinate system is particularly useful in sorting out trajectory-dependent from source- or sink-dependent effects. The representation is illustrated by applying it to the analysis of the nose structure protons observed by Smith and Hoffman (1974).