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This is a part of an ongoing project, the goal of which is to classify allsemi-direct products $\mathfrak s=\mathfrak g{\ltimes} V$ such that $\mathfrakg$ is a simple Lie algebra, $V$ is a $\mathfrak g$-module, and $\mathfrak s$has a free algebra of symmetric invariants. In this paper, we obtain such aclassification for the representations of the orthogonal and symplecticalgebras.

Semi-direct products involving $Sp_{2n}$ or $Spin_n$ with free algebras of symmetric invariants