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The geometric approach to sets of ordinary differential equations and Hamiltonian dynamicsThe calculus of differential forms is used to discuss the local integration theory of a general set of autonomous first order ordinary differential equations. Geometrically, such a set is a vector field V in the space of dependent variables. Integration consists of seeking associated geometric structures invariant along V: scalar fields, forms, vectors, and integrals over subspaces. It is shown that to any field V can be associated a Hamiltonian structure of forms if, when dealing with an odd number of dependent variables, an arbitrary equation of constraint is also added. Families of integral invariants are an immediate consequence. Poisson brackets are isomorphic to Lie products of associated CT-generating vector fields. Hamilton's variational principle follows from the fact that the maximal regular integral manifolds of a closed set of forms must include the characteristics of the set.
Document ID
19750043647
Acquisition Source
Legacy CDMS
Document Type
Reprint (Version printed in journal)
Authors
Estabrook, F. B.
Wahlquist, H. D.
(California Institute of Technology, Jet Propulsion Laboratory, Pasadena Calif., United States)
Date Acquired
August 8, 2013
Publication Date
April 1, 1975
Publication Information
Publication: SIAM Review
Volume: 17
Subject Category
Numerical Analysis
Accession Number
75A27719
Funding Number(s)
CONTRACT_GRANT: NAS7-100
Distribution Limits
Public
Copyright
Other

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