Transition and formation of the torque pattern of undulatory locomotion in resistive force dominated media

Abstract: In undulatory locomotion, torques along the body are required to overcome external forces from the environment and bend the body. Using a resistive force theory model, we find that the torque from external resistive forces has a traveling wave pattern with decreasing speed as the wave number (the number of wavelengths on the locomotor's body) increases from 0.5 to 1.8, and the torque transitions into a two-wave-like pattern and complex patterns as the wave number increases to values of 2 and greater values. Using phasor diagrams analysis, we reveal the formation and transitions of the pattern as the consequences of the integration and cancellation of force phasors.