The calculation of particle trajectories in the Earth's magnetic field has
been a subject of interest since the time of Stormer. The fundamental probl
em is that the trajectory-tracing process involves using mathematical equat
ions that have `no solution in closed form'. This difficulty has forced res
earchers to use the `brute force' technique of numerical integration of man
y individual trajectories to ascertain the behavior of trajectory families
or groups. As the power of computers has improved over the decades, the num
erical integration procedure has grown more tractable and while the problem
is still formidable, thousands of trajectories can be computed without the
expenditure of excessive resources. As particle trajectories are computed
and the characteristics analyzed we can determine the cutoff rigidity of a
specific location and viewing direction and direction and deduce the direct
ion in space of various cosmic ray anisotropies. Unfortunately, cutoff rigi
dities are not simple parameters due to the chaotic behavior of the cosmic-
ray trajectories in the cosmic ray penumbral region. As the computational p
roblem becomes more manageable, there is still the issue of the accuracy of
the magnetic field models. Over the decades, magnetic field models of incr
easing complexity have been developed and utilized. The accuracy of traject
ory calculations employing contemporary magnetic field models is sufficient
that cosmic ray experiments can be designed on the basis of trajectory cal
culations. However, the Earth's magnetosphere is dynamic and the most widel
y used magnetospheric models currently available are static. This means tha
t the greatest uncertainly in the application of charged particle trajector
ies occurs at low energies.