skew.exp {rotations}

Matrix exponential

Description

Compute the matrix exponential for skew-symmetric matrices according to the usual Taylor expansion. The expansion is significantly simplified for skew-symmetric matrices, see moakher02. Maps a matrix belonging to the lie algebra so(3) into the lie group SO(3).

Usage

skew.exp(x)

Arguments

x

single 3\times 3 skew-symmetric matrix or n\times 9 sample of skew-symmetric matrices.

Details

moakher02

Value

Matrix e^{\bm H} in SO(3) .

Examples

Rs <- ruars(20, rcayley)
lRs <- log(Rs)           #Take the matrix logarithm for rotation matrices
Rs2 <- skew.exp(lRs)     #Go back to rotation matrices
all.equal(Rs, Rs2)