Extent of redundancy in human movements under nonholonomic constraints can be an important factor to detemince a resulting movement. However, the redundancy has seldom been examined concretely in previous studies concerning optimality of human movements under such constraints. This study focuses on a gymnastic movement on the high bar, called "giant swing backward", as and almost periodic task under a second order nonholonomic constraint, and reveals a part of redundancy of the task by extending our prvious study. To this end, a simple dynamical model of an expert gymnast performing the giant swing back ward is constructed with parameterization of time histories of actuated joint angles by Fourier serires, and is confirmed to approximately reproduce a measured movement of the gymnast. The redundancy is calculated in various parameter spaces composed of lower order fourier coefficients. The results illustrate restricted but considerable redundancy underlying the giant swing backward. Moreover, within the set of the redundant movements, four kinds of optimization citeria are examined to explain the movement performed by the gymnast.