The curvature is useful in drawing a curve of H; the diameter of curvature D is given by
| D = | dp2 | = | ½k2 sin3 θ | , | ½D | = | ¼k2 | . |
| dp | δ − δ′ | p | KM·KN |
(48)
The curvature is zero and H passes through a point of inflexion when C′ comes into the horizontal plane through C; ψ will then be stationary and the curve described by C′ will be looped.
In a state of steady motion, z oscillates between two limits z2 and z3 which are close together; so putting z2 = z3 the coefficient of z in Z is
| 2Z1z3 + z23 = −1 + | GG′ | = −1 + | (OM cos θ + ON) (OM + ON cos θ) | , |
| A2n2 | OM·ON |
(49)
| 2z1z3 = | OM2 + ON2 | cos θ, z1 = | OM2 + ON2 | , |
| OM·ON | 2OM·ON |
(50)