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This paper contributes to the understanding of snake robot locomotion by employing nonlinear system analysis tools for investigating fundamental properties of snake robot dynamics. The paper has five contributions: 1) a partially feedback linearized model of a planar snake robot influenced by viscous ground friction is developed. 2) A stabilizability analysis is presented proving that any asymptotically stabilizing control law for a planar snake robot to an equilibrium point must be time-varying. 3) A controllability analysis is presented proving that planar snake robots are not controllable when the viscous ground friction is isotropic, but that a snake robot becomes strongly accessible when the viscous ground friction is anisotropic. The analysis also shows that the snake robot does not satisfy sufficient conditions for small-time local controllability (STLC). 4) An analysis of snake locomotion is presented that easily explains how anisotropic viscous ground friction enables snake robots to locomote forward on a planar surface. The explanation is based on a simple mapping from link velocities normal to the direction of motion into propulsive forces in the direction of motion. 5) A controller for straight line path following control of snake robots is proposed and a Poincaré map is investigated to prove that the resulting state variables of the snake robot, except for the position in the forward direction, trace out an exponentially stable periodic orbit.