6.26 two-mirror design relative to the incoming light. The issues raised by this requirement are discussed in Section VI.5. VI.5: THE PRECESSION/NUTATION PROBLEM VI.5.1: General Remarks: Figure 6.14 shows the desired orientation of the colony as it travels around the Sun. The figure also defines an axis useful to the discussion. The path of the Earth around the Sun defines the plane of the ecliptic. The q-axis is perpendicular to that plane. To keep the axis of symmetry of the colony pointed at the Sun at all times, that axis should be in the plane of the ecliptic and should rotate about the q-axis once per sidereal year. The term "axis of symmetry" is defined as the geometric axis through the tips of the endcaps. "Spin axis" or "z-axis" refers to the axis about which the colony spins--not necessarily the same as the axis of symmetry. This discussion first deals with the spinning hull and how to rotate its axis of symmetry about the q-axis. VI.5.2: The Hull as Gyroscope: A gyroscope is defined as a rotating body symmetrical about its spin axis. Our spinning hull approximated this in that it was almost symmetrical about its spin axis; the asymmetries would bring up the problem of nutation later but for clarity of discussion,the hull was first modeled as a pure gyro with its spin axis exactly on its axis of symmetry. Appendix VI.B presents a general discussion of the gyroscope, developing equations for moment of inertia, angular momentum, precession by torque, and angular deflection around the torque axis. Calculations leading to an estimate of the moment of inertia of the hull, agricultural dirt, human housing, machinery, and atmosphere about the spin axis (z-axis) appear in Appendix VI.C. Substituting that estimate into the equation for angular momentum:
RkJQdWJsaXNoZXIy MTU5NjU0Mg==