This paper investigates the dynamic behavior of an eccentric disk rolling on a curve of arbitrary shape and then on a curve defined as a cubic function. Comparisons are made to a disk without eccentricity and the related point mass approximation. The curve is subject to sinusoidal base excitation, and the system is considered from the perspective of a potential well problem where escape is possible on one side. The equations of motion are derived using a roll without slip constraint, and the behavior is investigated by means of approximate analytical solutions, numerically simulated frequency and amplitude sweeps, and by considering the basins of attraction when initial conditions or forcing parameters are varied. © 2013 Elsevier B.V. All rights reserved.