rotations (version 1.5)

skew.exp: 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 Moakher (2002). Maps a matrix belonging to the lie algebra $so(3)$ into the lie group $SO(3)$.

Usage

skew.exp(x)

Arguments

x

single $3-by-3$ skew-symmetric matrix or $n-by-9$ sample of skew-symmetric matrices.

Value

Matrix $e^H$ in $SO(3)$ .

References

Moakher M (2002). "Means and averaging in the group of rotations." SIAM Journal on Matrix Analysis and Applications, 24(1), pp. 1-16.

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)