On the Hamel Coefficients and the Boltzmann–Hamel Equations for the Rigid Body

Abstract The Boltzmann–Hamel (BH) equations are central in the dynamics and control of nonholonomic systems described terms quasi-velocities. rigid body is a classical example such systems, it well-known that BH-equations Newton–Euler (NE) when twists as It further known NE-equations Euler–Poincaré, respectively, reduced Euler–Lagrange on SE (3) using body-fixed or spatial representation twists. connection between these Hamel coefficients, which immediately identified structure constants (3). However, an explicit coordinate-free derivation has not been presented literature. In this paper coefficients for derived way without resorting to local coordinates describing motion. three most relevant choices quasi-velocities (body-fixed, spatial, hybrid twists) considered. corresponding explicitly rotating free floating body. Further, nonholonomically constrained bodies discussed, demonstrated inhomogenous ball rolling plane.