relations and, sometimes, this is very difficult to do using standard algorithms. In this paper we propose a general method to derive the equations defining the stratification of orbit spaces of CLG’s, in the form of explicit rational parametric relations.

3truemm This paper is organized as follows. In section 2 we summarize the results in the $P$-matrix approach to the characterization of the orbit spaces of CLG’s [@020; @020a]. In section 3 we present and prove our results, and in section 4, we illustrate them in a physically significant example, related to spontaneous polarization in chiral biaxial liquid crystals.

An overview of the geometry of linear group actions
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In this section, we shall recall, without proofs, some results concerning invariant theory and the geometry of orbit spaces of CLG’s (see, for instance, [@080; @710; @683] and references therein).

For our purposes, it will not be restrictive to assume that $G$ is a matrix subgroup of the group O(n), acting linearly in the Euclidean space $\real^{n}$ and thus defining the $G$-space $(G,\real^n)$.

We shall denote by $g\cdot x$ the action of $g\in G$ on $x\in\real^n$ and by $G_x$ the isotropy subgroup of $G$ at $x\in\real^n$. The isotropy subgroups of $G$ 