Notations
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:math:`q,\dot{q},\ddot{q}`: vectors of movements, speeds and accelerations in the physical coordinate system

:math:`\eta ,\dot{\eta },\ddot{\eta }`: vectors of generalized movements, speeds and accelerations

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

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

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

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

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

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

:math:`I`: identity matrix

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

:math:`t`: variable time, :math:`\omega`: variable pulsation

:math:`\text{TF}`: Fourier transform, :math:`{\text{TF}}^{-1}`: inverse Fourier transform

A+: pseudo-inverse of matrix A