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- W2000831194 abstract "Throughout the paper M will be a C” compact m-dimensional connected Riemannian manifold with a C” Riemannian metric ( , ), aA4 = q4 called the configuration space. The dimension m of A4 is called the degree of freedom, the tangent bundle 7’44 of M the velocity phase space and the cotangent bundle T*M of A4 the momentum phase space. The vector bundle isomorphism p: TM + T*M defined by p(u) w = (v, w ) is a C” diffeomorphism and will be referred to as the mass operator otherwise called the Legendre transformation. The function K: TM--+ R defined by K(v) = + (v, v ) is called the kinetic energy of the system. The constraint Z is a C” mapping qHZq which assigns to each qE M an n-dimensional subspace C, c T,M. The subvector bundle XM of TM defined by the vectors of all Z,, q E M, is a regular submanifold of TM, and if C,’ is the orthogonal complement of C,, in T,M, the same is true for the subvector bundle ZiM defined by the distribution q H Zi. The bundles CM, ELM have dimensions m + n, 2m n and there are canonically defined C” bundle mappings P: TM + CM, P’ : TM + 2” M defined by Pv, =: va, P’v, =: v,’ where vi, v: are the orthogonal projections of v, on C,, Zi. By means of the mass operator one can translate EM, Z’M, P," @default.
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- W2000831194 date "1986-07-01" @default.
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- W2000831194 title "Dissipative systems with constraints" @default.
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- W2000831194 doi "https://doi.org/10.1016/0022-0396(86)90061-6" @default.
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