To solve the LBCE using equation (3), we now need to
expand functions of the form 
in
action-angle variables. Specifically, for a spherical system, it is
easy to write down the description of a particle orbit in the orbital
plane. From this, we may derive the general harmonic expansion
following the technique presented in Tremaine & Weinberg
(1984). This yields
where 
is the elevation of the orbital plane defined by the
actions 
, W is
with 
, and 
is rotation
matrix for spherical harmonics (e.g. Edmonds 1960).