This paper investigates methods for steering systems with nonholonomic constraints between arbitrary configurations. It builds on early work by Brockett, who derived optimal controls for canonical systems where the configuration space is spanned by input vector fields and their first-order Lie brackets. The authors derive suboptimal trajectories for systems that are not in canonical form and consider systems where multiple levels of bracketing are needed to achieve controllability. These trajectories use sinusoids at integrally related frequencies to achieve motion at a given bracketing level. The paper defines a class of systems that can be steered using sinusoids (chained systems) and provides conditions under which a class of two-input systems can be converted into this form. The authors also discuss the controllability of these systems and present examples to illustrate the proposed methods.This paper investigates methods for steering systems with nonholonomic constraints between arbitrary configurations. It builds on early work by Brockett, who derived optimal controls for canonical systems where the configuration space is spanned by input vector fields and their first-order Lie brackets. The authors derive suboptimal trajectories for systems that are not in canonical form and consider systems where multiple levels of bracketing are needed to achieve controllability. These trajectories use sinusoids at integrally related frequencies to achieve motion at a given bracketing level. The paper defines a class of systems that can be steered using sinusoids (chained systems) and provides conditions under which a class of two-input systems can be converted into this form. The authors also discuss the controllability of these systems and present examples to illustrate the proposed methods.