Barrett, D.I.Biggs, RoryRemsing, C.C.2018-09-202018-04Barrett, D.I., Biggs, R. & Remsing, C.C. Quadratic Hamilton–Poisson Systems on se(1,1)∗−: The Inhomogeneous Case. Acta Applicandae Mathematicae (2018) 154: 189-230. https://doi.org/10.1007/s10440-017-0140-3.0167-8019 (print)1572-9036 (online)10.1007/s10440-017-0140-3http://hdl.handle.net/2263/66610We consider equivalence, stability and integration of quadratic Hamilton–Poisson systems on the semi-Euclidean Lie–Poisson space se(1,1)∗−. The inhomogeneous positive semidefinite systems are classified (up to affine isomorphism); there are 16 normal forms. For each normal form, we compute the symmetry group and determine the Lyapunov stability nature of the equilibria. Explicit expressions for the integral curves of a subclass of the systems are found. Finally, we identify several basic invariants of quadratic Hamilton–Poisson systems.en© Springer Science+Business Media B.V., part of Springer Nature 2017. The original publication is available at : http://link.springer.comjournal/10440.Hamilton–Poisson systemLie–Poisson spaceLyapunov stabilityPoisson equationEuclideanHamiltonsIntegral curvesNormal formPositive semidefiniteSymmetry groupsSystem stabilityPostprint Article