The Euler-Lagrange equations, while universal, are not always effective for analyzing mechanical systems. For example, it is difficult to study the motion of the Euler top if the Euler-Lagrange equations are used to represent the dynamics. On the other hand, Euler’s representation of the rotational dynamics of a rigid body is much more effective but does not appear as universal and systematic. Poincare in 1902 made Euler’s approach systematic for systems on Lie groups. Hamel in 1904 extended Poincare’s result to finite-dimensional mechanics on arbitrary configuration spaces. This talk introduces Hamel’s formalism for infinite-dimensional systems, such as continuum media, in the form of ordinary differential equations on infinite-dimensional manifolds and with an emphasis on the continuum mechanics with velocity constraints.