  O'Hara introduced several functionals as knot energies. One of them is the
M\"{o}bius energy. We know its M\"{o}bius invariance from Doyle-Schramm's
cosine formula. It is also known that the M\"{o}bius energy was decomposed into
three components keeping the M\"{o}bius invariance. The first component of
decomposition represents the extent of bending of the curves or knots, while
the second one indicates the extent of twisting. The third one is an absolute
constant. In this paper, we show a similar decomposition for generalized O'Hara
energies. On the way to derive it, we obtain an analogue of the cosine formula
for the generalized O'Hara energy. Furthermore, using decomposition, the first
and second variational formulae are derived.
