Transverse displacement of the electron beam at input to the wiggler induces betatron oscillation, imparting a sinusoidal transverse displacement to the gain medium seen by the optical beam. As the light propagates down this ''rippled'' medium it is guided by the dispersion, thereby acquiring some transverse sinusoidal displacement. At output from the wiggler the optical beam in general has acquired some transverse component of velocity, that is, it propagates off-axis. As the e-beam displacement fluctuates statistically with every pulse, the optical output direction jitters around the nominal axis. The jitters is estimated with a model that includes off-axis optical propagation through a ''rippled'' gain medium but neglects feedback of the off-axis light on the e-beam. The model is solved in perturbation theory. The jitter is calculated at the final aperture of the optical system beyond the wiggler. 8 refs., 13 figs.

Rephrasing the equations of motion for orbital maneuvers in terms of Lagrangian generalized coordinates instead of Newtonian rectangular cartesian coordinates can make certain harmonic terms in the orbital angular momentum vector more readily apparent. In this formulation the equations of motion adopt the form of a damped harmonic oscillator when torques are applied to the orbit in a variationally prescribed manner. The frequencies of the oscillator equation are in some ways unexpected but can nonetheless be exploited through resonant forcing functions to achieve large secular variations in the orbital elements. Two cases are discussed using a circular orbit as the control case: (1) large changes in orbital inclination achieved by harmonic excitation rather than one impulsive velocity change, and (2) periodic and secular changes to the longitude of the ascending node using both stable and unstable excitation strategies. The implications of these equations are also discussed for both artificial satellites and natural satellites. For the former, two utilitarian orbits are suggested, each exploiting a form of harmonic excitation. 5 refs.