A general model is proposed which accounts for the dynamical evolution of the observed jets, envelopes and tail bands of periodic Comet Swift-Tuttle, the parent comet of the Perseid meteor stream, in terms of dust ejection from discrete active regions on the rotating nucleus. High-resolution drawings and measurements of cometary jets made upon the comet's first appearance in 1862 are used to infer a nuclear rotation period of 2.77 days, obliquity of 80 deg, and spin axis orientation with respect to the solar direction of 60 deg. The observed jets are attributed to eight discrete active regions covering not more than 1% of the cometary surface and producing bursts of duration of about 0.1 day. Calculations show that waning dust jets develop into envelopes and that old envelopes in turn become the observed tail bands. No evidence of truly violent explosions is found, and effects of active region outgassing on cometary orbital motion are negligible. Potential applications of the model to periodic Comet Halley and other comets are noted.