  We investigate the long-term orbital dynamics of spinless extended bodies in
Schwarzschild geometry, and show that periodic deviations from spherical
symmetry in the shape of a test body may trigger the onset of chaos. We do this
by applying Dixon's formalism at quadrupolar order to a nearly spherical body
whose shape oscillates between a prolate and an oblate spheroid. The late-time
chaotic behavior is then verified by applying Melnikov's method.

General Relativity and Quantum Cosmology;Chaotic Dynamics