The steady motion and nutation superposed may be expressed by
θ = α + L, sin θ = sin α + L cos α, cos θ = cos α − L sin α, Ω = μ + N, r = R + Q,
(1)
where L, N, Q are small terms, involving a factor enti, to express the periodic nature of the nutation; and then if a, c denote the mean value of x, z, at the point of contact
x = a + Lρ cos α, z = c − Lρ sin α,
(2)
x sin θ + z cos θ = a sin α + c cos α + L (a cos α − c sin α),
(3)
x cos θ − z sin θ = a cos α − c sin α − L (a sin α + c cos α − ρ).
(4)