On Lagrangian groups
نویسندگان
چکیده
منابع مشابه
Symmetry Reduction of Discrete Lagrangian Mechanics on Lie Groups
For a discrete mechanical system on a Lie group G determined by a (reduced) Lagrangian l we define a Poisson structure via the pull-back of the Lie-Poisson structure on the dual of the Lie algebra g∗ by the corresponding Legendre transform. The main result shown in this paper is that this structure coincides with the reduction under the symmetry group G of the canonical discrete Lagrange 2-form...
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In this paper, we provide controllability tests and motion control algorithms for underactuated mechanical control systems on Lie groups with Lagrangian equal to kinetic energy. Examples include satellite and underwater vehicle control systems with the number of control inputs less than the dimension of the configuration space. Local controllability properties of these systems are characterised...
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The purpose of this note is to give a classification of the orbital structure of certain reductive group actions on the Lagrangian Grassmanian. The groups under consideration are Sp × Sp and GL. In general, the finiteness of orbits is known ( [8], [1], [9], [2], [10]). However, the homogeneous structure of each individual orbit is not known except perhaps the generic open orbit 1. The main resu...
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This is a part of the Advanced Mechanics course MA2341. These notes are partially based on the textbook “Mechanics” by L.D. Landau and E.M. Lifshitz. ∗Email: [email protected] † Correspondent fellow at Steklov Mathematical Institute, Moscow.
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This article uses Cartan-Kähler theory to show that a small neighborhood of a point in any surface with a Riemannian metric possesses an isometric Lagrangian immersion into the complex plane (or by the same argument, into any Kähler surface). In fact, such immersions depend on two functions of a single variable. On the other hand, explicit examples are given of Riemannian three-manifolds which ...
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ژورنال
عنوان ژورنال: Transactions of the American Mathematical Society
سال: 1973
ISSN: 0002-9947
DOI: 10.1090/s0002-9947-1973-0318312-7