The coupled nonlinear oscillating systems studied do not possess linear normal modes. The nonlinearly related modes of
$m1x¨1+∑k=1nakx1k+∑k=1nAk(x1−x2)k=0m2x¨2+∑k=1nbkx2k−∑k=1nAk(x1−x2)k=0(1)$

$withk=1,3,5,......$
are expressed as superpositions of the linear normal modes of each of the homogeneous systems of the form
$m1x¨1+akx1k+Ak(x1−x2)k=0m2x¨2+bkx2k−Ak(x1−x2)k=0(2)$
whose force fields are superimposed to yield the force field of equations (1).
This content is only available via PDF.