P‐positive definite matrices and stability of nonconservative systems

The bifurcation problem of constrained non-conservative systems with non symmetric stiffness matrices is investigated. It leads to study the subset D p,n of M n(R) of the so called p-positive definite matrices (1 ≤ p ≤ n). The main result (D 1,n ⊂ D p,n) is proved, the reciprocal result is investigated and the consequences on the stability of elastic nonconservative systems are highlighted.