PolarDecomp: Polar Decomposition
In geophys: Geophysics, Continuum Mechanics, Gravity Modeling

Description Usage Arguments Details Value Author(s) References See Also Examples

Polar Decomposition for Strain

1	PolarDecomp(A)

`A`	Strain Matrix

Polar decomposition uses the svd to extract 2 matrices that represent the stretch and rotation of a strain: A = UP. U is orthogonal rotation matrix and P is the stretch tensor. These are extracted from the singular value decomposition.

`P`	matrix, stretch tensor
`U`	matrix, orthogonal rotation matrix

Jonathan M. Lees<jonathan.lees@unc.edu>

<http://en.wikipedia.org/wiki/Finite_strain_theory>

svd

A = matrix(runif(4, -1, 1), ncol=2)
PD = PolarDecomp(A)

E = svd(A)

###  W         S           V
 E$u 

 ###t(E$v) %*% diag(E$d)%*%  (E$u)

P = E$v
U =  E$u 


U