The editors have organized the seventeen selections that make up the main body of the text in two parts devoted to second-order decomposition models for image processing, optimizing spatial and tonal data for PDE-based inpainting, and other subjects; and the Purcell three-link swimmer, controllability of Keplerian motion
with low-thrust control systems, and other related subjects.
Remaining chapters formally describe dynamical symmetry in Hamiltonian mechanics, symmetries in classical Keplerian motion
, dynamical symmetry in Schrodinger quantum mechanics, spectrum-generating Lie algebras and groups admitted by Schrodinger equations, dynamical symmetry of regularized hydrogen-like atoms, approximate dynamical symmetries in atomic and molecular physics, rovibronic systems, and dynamical symmetry of Maxwell's equations.
and the first term GMm/r now describes the potential of a homogeneous sphere and thus refers to Keplerian motion
, the remaining part represents the Earth's oblateness via the zonal harmonic coefficients and 
Essentially, the method involves writing the equations of motion as the sum of a part that describes the independent Keplerian motion
of the bodies about the Sun plus a part (called the disturbing function) that contains terms due to the pairwise interactions among the planets and minor bodies and the indirect terms associated with the back-reaction of the planets on the Sun.
In the late 1960s Marsden confirmed that comets do in fact depart from pure Keplerian motion
around the Sun.
Although the relative sizes and distances of the objects were shrunk and scaled, the Keplerian motion
was kept unchanged and at the true relative rates.
They find Keplerian motion
in a disk extending to 500 astronomical units (500 times the earth's distance from the sun, or about 50 billion miles) out from the star.