Journal ArticleDOI
Linear Hamiltonian systems are integrable with quadratics
Huseyin Kocak,Huseyin Kocak +1 more
TLDR
In this paper, a new proof of a theorem of Williamson on the complete integrability of time-independent, real, linear Hamiltonian differential equations with quadratic integrals is given.Abstract:
A new proof of a theorem of Williamson on the complete integrability of time‐independent, real, linear Hamiltonian differential equations with quadratic integrals is given. The sets where these integrals are functionally dependent are explicitly found.read more
Citations
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Topology and mechanics with computer graphics
TL;DR: In this article, the global topology of constant energy surfaces of Hamiltonian systems in four dimensions was investigated using techniques of computer graphics, and the topology was shown to have a constant number of vertices.
Journal ArticleDOI
Linear Hamiltonian Systems: Quadratic Integrals, Singular Subspaces and Stability
TL;DR: In this paper, a chain of quadratic first integrals of general linear Hamiltonian systems that have not been represented in canonical form is found and their involutiveness is established and the problem of their functional independence is studied.
Journal ArticleDOI
On the construction of transformations of linear hamiltonian systems to real normal forms
Eric A. Butcher,Subhash C. Sinha +1 more
TL;DR: Several possible arrangements of the suggested transformations are given which result in the various normal forms derived previously as well as in a few new ones for degenerate cases which have not appeared before.
References
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Book
Mathematical Methods of Classical Mechanics
TL;DR: In this paper, Newtonian mechanics: experimental facts investigation of the equations of motion, variational principles Lagrangian mechanics on manifolds oscillations rigid bodies, differential forms symplectic manifolds canonical formalism introduction to pertubation theory.
Book
The Theory of Matrices
TL;DR: In this article, the Routh-Hurwitz problem of singular pencils of matrices has been studied in the context of systems of linear differential equations with variable coefficients, and its applications to the analysis of complex matrices have been discussed.
Book
Introduction to Lie Algebras and Representation Theory
TL;DR: In this paper, Semisimple Lie Algebras and root systems are used for representation theory, isomorphism and conjugacy theorem, and existence theorem for representation.
Book
Foundations of mechanics
TL;DR: In this article, Ratiu and Cushman introduce differential theory calculus on manifolds and derive an overview of qualitative and topological properties of differentiable properties of topological dynamics.