کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
1898989 | 1044817 | 2006 | 40 صفحه PDF | دانلود رایگان |
عنوان انگلیسی مقاله ISI
Cartan forms for first order constrained variational problems
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کلمات کلیدی
موضوعات مرتبط
مهندسی و علوم پایه
ریاضیات
فیزیک ریاضی
پیش نمایش صفحه اول مقاله
![عکس صفحه اول مقاله: Cartan forms for first order constrained variational problems Cartan forms for first order constrained variational problems](/preview/png/1898989.png)
چکیده انگلیسی
Given a constrained variational problem on the 1-jet extension J1Y of a fibre bundle p:YâX, under certain conditions on the constraint submanifold SâJ1Y, we characterize the space of admissible infinitesimal variations of an admissible section s:XâY as the image by a certain first order differential operator, Ps, of the space of sections Î(X,sâVY). In this way we obtain a constrained first variation formula for the Lagrangian density LÏ on J1Y, which allows us to characterize critical sections of the problem as admissible sections s such that Ps+ELÏ(s)=0, where Ps+ is the adjoint operator of Ps and ELÏ(s) is the Euler-Lagrange operator of the Lagrangian density LÏ as an unconstrained variational problem. We introduce a Cartan form on J2Y which we use to generalize the Cartan formalism and Noether theory of infinitesimal symmetries to the constrained variational problems under consideration. We study the relation of this theory with the Lagrange multiplier rule as well as the question of regularity in this framework. The theory is illustrated with several examples of geometrical and physical interest.
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Journal of Geometry and Physics - Volume 56, Issue 4, April 2006, Pages 571-610
Journal: Journal of Geometry and Physics - Volume 56, Issue 4, April 2006, Pages 571-610
نویسندگان
P.L. GarcÃa, A. GarcÃa, C. Rodrigo,