2. Notations

\(q,\dot{q},\ddot{q}\): vectors of movements, speeds and accelerations in the physical coordinate system

\(\eta ,\dot{\eta },\ddot{\eta }\): vectors of generalized movements, speeds and accelerations

\(F\): matrix made up of the projection base vectors (displacements)

\({\Phi }_{\epsilon }\): matrix formed from the projection base vectors (deformations)

\({\Phi }_{\sigma }\): matrix formed from the projection base vectors (constraints)

\(\stackrel{ˉ}{\Phi }\): matrix of basic vectors (displacements), restricted to measured degrees of freedom

\({\stackrel{ˉ}{\Phi }}_{\epsilon }\): matrix of basic vectors (deformations), restricted to measured degrees of freedom

\({\stackrel{ˉ}{\Phi }}_{\sigma }\): matrix of basic vectors (constraints), restricted to measured degrees of freedom

\(I\): identity matrix

\({N}_{\text{num}}\): number of projection base vectors, \({N}_{\text{exp}}\): number of degrees of freedom measured

\(t\): variable time, \(\omega\): variable pulsation

\(\text{TF}\): Fourier transform, \({\text{TF}}^{-1}\): inverse Fourier transform

A+: pseudo-inverse of matrix A