Concepedia

A geometric setting for higher-order Dirac–Bergmann theory of constraints

Journal of Mathematical Physics · 1994 · 26 citations · 13 references

Concepts

Hamiltonian TheoryEngineeringRiemann-hilbert ProblemConstrained SystemsDiscrete Dynamical SystemGeometric MeaningMechanical SystemsNonlinear Mechanical SystemGeometric SettingComputational MechanicsHamiltonian SystemLagrangian MethodHamilton Equations

Abstract

Hamilton equations for degenerate time-dependent, and generally higher-order mechanical systems are considered and their geometric meaning is analyzed. The local dynamics of constrained systems is clarified and an algorithm for finding it is presented.

References

13

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The Hamilton-Cartan formalism in the calculus of variations

Hubert Goldschmidt, Shlomo Sternberg · Annales de l’institut Fourier · 1973 · 427 citations · Full text

Hamiltonian Theory, Several Variables, Engineering +9

Presymplectic manifolds and the Dirac–Bergmann theory of constraints

Mark J. Gotay, James M. Nester, George Libby Hinds · Journal of Mathematical Physics · 1978 · 320 citations

Generalized Hamilton-type Equations, Hamiltonian Theory, Form ι +6

On the Existence of Global Variational Principles

Ian Anderson, T. Duchamp · American Journal of Mathematics · 1980 · 181 citations

Variational Analysis, Global Variational Principles, Functional Analysis +2

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A. M. Vinogradov · Journal of Mathematical Analysis and Applications · 1984 · 176 citations

Spectral Theory, Hamiltonian Theory, Engineering +7