where α, β, γ are arbitrary constants. Substituting in (23) we find
| ( 1 + | M0a2 | ) ẋ = | a | (βz − γy), ( 1 + | M0a2 | ) ẏ = | a | (γx − αz), ( 1 + | M0a2 | ) ż = | a | (αy − βx). |
| C | c | C | c | C | c |
(25)
Hence αẋ + βẏ + γż = 0, or
αx + βy + γz = const.;
(26)
which shows that the centre of the rolling sphere describes a circle. If the axis of z be taken normal to the plane of this circle we have α = 0, β = 0, and
| ( 1 + | M0a2 | ) ẋ = −γ | a | y, ( 1 + | M0a2 | ) ẏ = γ | a | x. |
| C | c | C | c |
(27)
The solution of these equations is of the type