کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
5773642 1413515 2017 16 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
Deformation of piecewise differentiable curves in constrained variational calculus
ترجمه فارسی عنوان
تغییر شکل منحنی های متفاوت تناوبی در محاسبات تناوبی محدود
موضوعات مرتبط
مهندسی و علوم پایه ریاضیات آنالیز ریاضی
چکیده انگلیسی
A survey of the geometric tools involved in the study of constrained variational calculus is presented. The central issue is the characterization of the admissible deformations of piecewise differentiable sections of a fibre bundle Vn+1→R, in the presence of arbitrary non-holonomic constraints. Asynchronous displacements of the corners are explicitly considered. The coordinate-independent representation of the variational equation and the associated concepts of infinitesimal control and absolute time derivative are reviewed. In the resulting algebraic environment, every admissible section is assigned a corresponding abnormality index, identified with the co-rank of a suitable linear map. Sections with vanishing index are called normal. A section is called ordinary if every solution of the variational equation vanishing at the endpoints is tangent to some finite deformation with fixed endpoints. The interplay between abnormality index and ordinariness - in particular the fact that every normal evolution is automatically an ordinary one - is discussed.
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Differential Geometry and its Applications - Volume 54, Part A, October 2017, Pages 298-313
نویسندگان
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