Gesamtgesetz der Rotations- und Bahnmechanik in der A–B–C‑Magnetarchitektur

$$\boxed{{\displaystyle {\omega }_B(t)=[{\omega }_{\text{block}}(r,{\phi }_A)+{\omega }_{\text{roll}}(v_A,{\phi }_A)]+\frac{r}{I_B}{F}_{C,\theta }(r,\theta )}}$$

mit

$$F_{C,\theta }(r,\theta )=-\frac{1}{r}\frac{\mathrm{\partial }{\mathrm{\Phi }}_C(r,\theta )}{\mathrm{\partial }\theta },F_{C,r}(r)=-\frac{\mathrm{\partial }{\mathrm{\Phi }}_C(r)}{\mathrm{\partial }r},F_{C,z}\approx 0,$$

und der Bahnführungsbedingung

$$m_B{\omega }_{\text{orb}}^{2}r=\mid -\frac{\mathrm{\partial }{\mathrm{\Phi }}_C(r)}{\mathrm{\partial }r}\mid \mathrm{.}$$

Die Gesamtrotation ergibt sich damit aus

$${\omega }_B={\omega }_{B,AB}+{\omega }_{B,C},$$

wobei

$${\omega }_{B,AB}={\omega }_{\text{block}}(r,{\phi }_A)+{\omega }_{\text{roll}}(v_A,{\phi }_A),{\omega }_{B,C}=\frac{r}{I_B}{F}_{C,\theta }(r,\theta )\mathrm{.}$$

The A‑induced rotational contributions ${\omega }_{\text{tilt}}$ and ${\omega }_{\text{drift}}$ are only defined for lateral tilt angles of A that are neither 0° nor 90°. At 0° the field is symmetric and produces no torque; at 90° the B‑magnet adheres to A instead of entering a free rotational regime.