Gibbs Notation supplement _2_

Gibbs Notation supplement _2_ - GibbsNotationandthe...

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Gibbs Notation and the operator Rank: Rank can be used to define the quantity type, i.e scalar, vector, tensor… Rank 0: A symbol of rank 0 is a scalar. This is only a value, and has no direction, but is only a magnitude. Examples: Pressure, Temperature, etc… Rank 1: A symbol of rank 1 is a vector. The value has both a magnitude and a direction. In an orthonormal system, it has three components. Example: Velocity, Heat Flux, etc… Rank 2: A symbol of rank 2 is a tensor. A tensor is a 3x3 matrix of values consisting of nine elements. Examples: Shear Stress, Shear Strain, etc… Higher ranks are beyond the scope of this course. The Operator: The ׏ operator is a vector quantity (rank 1) and is independent of coordinate system. This operator is useful because it allows one to express equations in different orthonormal coordinate systems with one equation. Note, it is an operator, and not a value; therefore, it must operate on a quantity. In Cartesian coordinates, it can be defined as:
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This note was uploaded on 09/05/2011 for the course EAS 4101 taught by Professor Sheplak during the Spring '08 term at University of Florida.

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Gibbs Notation supplement _2_ - GibbsNotationandthe...

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