Aspects of Differential Geometry and Tensor Calculus in Anholonomic Configuration Space

Abstract

In the context of finite deformation mechanics, a tangent mapping is anholonomic over some domain when it is not a gradient of a motion; conversely, a deformation gradient is holonomic when it is integrable to a motion field everywhere in that domain. This brief report addresses covariant differentiation for four possible choices of basis vectors in anholonomic space. As an example from continuum physics, the theory is applied towards description of divergence of the heat flux.

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Document Details

Document Type
Technical Report
Publication Date
Feb 01, 2013
Accession Number
ADA582371

Entities

People

  • John D. Clayton

Organizations

  • United States Army Research Laboratory

Tags

Communities of Interest

  • Weapons Technologies

DTIC Thesaurus Topics

  • Abstracts
  • Calculus
  • Coordinate Systems
  • Curvature
  • Department Of Defense
  • Differential Geometry
  • Geometry
  • Heat Flux
  • Heat Transfer
  • Materials
  • Mathematics
  • Mechanics
  • Military Research
  • Physics
  • Tensor Analysis
  • Tensors
  • Thermal Conductivity

Readers

  • Fluid Dynamics.
  • Graph Algorithms and Convex Optimization.

Technology Areas

  • Space
  • Space - Spacecraft Maneuvers