Discrete Lagrangian and Hamiltonian mechanics on Lie groupoids
نویسندگان
چکیده
منابع مشابه
Discrete Lagrangian and Hamiltonian Mechanics on Lie Groupoids
The purpose of this paper is to describe geometrically discrete Lagrangian and Hamiltonian Mechanics on Lie groupoids. From a variational principle we derive the discrete Euler-Lagrange equations and we introduce a symplectic 2-section, which is preserved by the Lagrange evolution operator. In terms of the discrete Legendre transformations we define the Hamiltonian evolution operator which is a...
متن کاملDiscrete Nonholonomic Lagrangian Systems on Lie Groupoids
This paper studies the construction of geometric integrators for nonholonomic systems. We derive the nonholonomic discrete Euler-Lagrange equations in a setting which permits to deduce geometric integrators for continuous nonholonomic systems (reduced or not). The formalism is given in terms of Lie groupoids, specifying a discrete Lagrangian and a constraint submanifold on it. Additionally, it ...
متن کاملDiscrete Hamilton–pontryagin Mechanics and Generating Functions on Lie Groupoids
We present a discrete analog of the recently introduced Hamilton– Pontryagin variational principle in Lagrangian mechanics. This unifies two, previously disparate approaches to discrete Lagrangian mechanics: either using the discrete Lagrangian to define a finite version of Hamilton’s action principle, or treating it as a symplectic generating function. This is demonstrated for a discrete Lagra...
متن کاملVariational Discrete Dirac Mechanics—implicit Discrete Lagrangian and Hamiltonian Systems
We construct discrete analogues of Tulczyjew’s triple and induced Dirac structures by considering the geometry of symplectic maps and their associated generating functions. We demonstrate that this framework provides a means of deriving implicit discrete Lagrangian and Hamiltonian systems, while incorporating discrete Dirac constraints. In particular, this yields implicit nonholonomic Lagrangia...
متن کاملSymmetry 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...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Nonlinearity
سال: 2006
ISSN: 0951-7715,1361-6544
DOI: 10.1088/0951-7715/19/6/006