Kinematic Analysis Based on Motion Group and its Lie Algebra.
نویسندگان
چکیده
منابع مشابه
On an Isospectral Lie-Poisson System and Its Lie Algebra
In this paper we analyse the matrix differential system X ′ = [N,X], where N is skew-symmetric and X(0) is symmetric. We prove that it is isospectral and that it is endowed with a Poisson structure, and discuss its invariants and Casimirs. Formulation of the Poisson problem in a Lie–Poisson setting, as a flow on a dual of a Lie algebra, requires a computation of its faithful representation. Alt...
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Let V be a finite-dimensional vector space, and let G be a subgroup of GL( V). Set D( V) equal to the algebra of differential operators on V with polynomial coefficients and D( V) G equal to the G invariants in D( V). If 9 is a reductive Lie algebra over C then ~ egis a Cartan subgroup of g, and if G is the adjoint group of 9 then W is the Weyl group of (g, ~) , Harish-Chandra introduced an alg...
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We define Lie groups and Lie algebras and show how invariant vector fields on a Lie group form a Lie algebra. We prove that this correspondence respects natural maps and discuss conditions under which it is a bijection. Finally, we introduce the exponential map and use it to write the Lie group operation as a function on its Lie algebra.
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ژورنال
عنوان ژورنال: TRANSACTIONS OF THE JAPAN SOCIETY OF MECHANICAL ENGINEERS Series C
سال: 2000
ISSN: 0387-5024,1884-8354
DOI: 10.1299/kikaic.66.1927