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IMA Journal of Mathematical Control and Information 1984 1(2):185-198; doi:10.1093/imamci/1.2.185
© 1984 by Institute of Mathematics and its Applications
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Linearization of Hamiltonian and Gradient Systems

A. J. van der SCHAFT

Department of Applied Mathematics, Twente University of Technology P.O. Box 217, 7500 AE Enschede, Holland

Necessary and sufficient conditions are derived in order to transform a nonlinear Hamiltonian or gradient system by a change of coordinates of its state space into a linear Hamiltonian or gradient system. It is shown that such a transformation necessarily respects the symplectic or metrical structure. The conditions are given in terms of the observation space of the system, which in the Hamiltonian case is a Lie algebra and in the gradient case a symmetric algebra.


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