Based on the equations of motion for linked rigid bodies that we derived recently [G. Kneller and K. Hinsen, Phys. Rev. E 50, 1559 (1994)], we develop a technique for the simulation of molecular systems with constraints. We apply it to analyze the importance of the various degrees of freedom of a polypeptide chain for its dynamics. We find that keeping the peptide planes rigid does not change the dynamics much, but that the bending degrees of freedom of the α-carbon bond geometry are essential for large-amplitude backbone motions. This means that the φ and ψ angles commonly used to characterize protein conformations and protein backbone dynamics do not constitute a sufficient set of variables to perform dynamical simulations.