DefineTriads[a,b,rm]

DefineTriads[{a1,b1,rm1}, ..., {an,bn,rmn}]

a,a1, ..., an: names of declared triads

b,b1, ..., bn: names of declared triads

rm,rm1, ..., rmn: rotation-matrix specifications

The function DefineTriads defines a direct relation between two declared triads by specifying the rotation matrix from the first triad to the second triad. A pair of indirectly related triads may not be defined.

The function DefineTriads results in permanent changes to the global variables GlobalTriadDeclarations and GlobalTriadDefinitions.

The syntax of a rotation-matrix specification corresponds to that of the argument to the MakeRotations procedure.

Restart;
DeclareTriads[a,b,c];
DefineTriads[{a,b,phi,1},{b,c,{q3,2},{Pi/2,3}}];
GlobalTriadDeclarations

$\left\{a\to \left\{b\right\},b\to \left\{a,c\right\},c\to \left\{b\right\}\right\}$

GlobalTriadDefinitions

$\left\{\left\{a,b\right\}\to \left\{\left\{1,0,0\right\},\left\{0,\mathrm{Cos}\left[\mathrm{phi}\right],-\mathrm{Sin}\left[\mathrm{phi}\right]\right\},\left\{0,\mathrm{Sin}\left[\mathrm{phi}\right],\mathrm{Cos}\left[\mathrm{phi}\right]\right\}\right\},\left\{b,a\right\}\to \left\{\left\{1,0,0\right\},\left\{0,\mathrm{Cos}\left[\mathrm{phi}\right],\mathrm{Sin}\left[\mathrm{phi}\right]\right\},\left\{0,-\mathrm{Sin}\left[\mathrm{phi}\right],\mathrm{Cos}\left[\mathrm{phi}\right]\right\}\right\},\left\{b,c\right\}\to \left\{\left\{0,-\mathrm{Cos}\left[\mathrm{q3}\right],\mathrm{Sin}\left[\mathrm{q3}\right]\right\},\left\{1,0,0\right\},\left\{0,\mathrm{Sin}\left[\mathrm{q3}\right],\mathrm{Cos}\left[\mathrm{q3}\right]\right\}\right\},\left\{c,b\right\}\to \left\{\left\{0,1,0\right\},\left\{-\mathrm{Cos}\left[\mathrm{q3}\right],0,\mathrm{Sin}\left[\mathrm{q3}\right]\right\},\left\{\mathrm{Sin}\left[\mathrm{q3}\right],0,\mathrm{Cos}\left[\mathrm{q3}\right]\right\}\right\}\right\}$

DeclarePoints, DeclareTriads, DefineObservers, DefinePoints