TITLE: Orbits of real groups, canonical forms of matrices
QUESTION [9 upvotes]: There are a lot of results in textbooks concerned with canonical forms of matrices under certain complex groups of transformations, e.g. GL(n|C), O(n|C),... 
Could anybody give me references where the canonical forms of real matrices under the action of SO(p,q|R) were found. Of most interest is the canonical form of antisymmetric matrices, i.e. that of the adjoint representation. Other related results, e.g. on canonical forms under SU(p,q), SP(p,q) are also appreciated. Thanks!

REPLY [5 votes]: Another reference is: D. Djokovic, J. Patera, P. Winternitz, H. Zassenhaus, Normal forms of elements of classical real and complex Lie and Jordan algebras, J. Math. Phys. 24 (1983), N6, 1363-1374 http://dx.doi.org/10.1063/1.525868 .