Review of investigations performed in the USSR on close approaches of comets to Jupiter and the evolution of cometary orbits

Methods are reviewed for calculating the evolution of cometary orbits with emphasis on the orbital changes that take place when comets pass within the spheres of action of giant planets. Topics discussed include: differences and difficulties in methods used for the calculation of large perturbations by Jupiter; the construction of numerical theories of motion covering the whole period of observations of each comet, allowing for planetary perturbations and the effects of nongravitational forces; and investigations of the evolution of cometary orbits over the 400 year interval 1660-2060. The classical theory of cometary capture is briefly discussed.