Continuous and Discrete Clebsch Variational Principles
نویسندگان
چکیده
منابع مشابه
Continuous and Discrete Clebsch Variational Principles
The Clebsch method provides a unifying approach for deriving variational principles for continuous and discrete dynamical systems where elements of a vector space are used to control dynamics on the cotangent bundle of a Lie group via a velocity map. This paper proves a reduction theorem which states that the canonical variables on the Lie group can be eliminated, if and only if the velocity ma...
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where the sum is performed for k ∈ Z and on indices i ∈ Z such that iε ∈ Ω and (i+ k)ε ∈ Ω. If we picture the lattice εZ ∩ Ω as the reference configuration of a set of material points interacting through some forces, and ui represents the displacement of the i-th point, then ψ ε can be thought as the energy density of the interaction of points with distance kε in the reference lattice. Note tha...
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ژورنال
عنوان ژورنال: Foundations of Computational Mathematics
سال: 2007
ISSN: 1615-3375,1615-3383
DOI: 10.1007/s10208-007-9022-9