An extension to the collisional model of the energetic cost of support qualitatively explains trotting and the trot–canter transition - Usherwood, James R. (J Exp Zool A Ecol Integr Physiol, 2019)
The majority of terrestrial mammals adopt distinct, discrete gaits across their speed range. Though there is evidence that walk, trot and gallop may be selected at speeds consistent with minimizing metabolic cost (Hoyt and Taylor, 1981, Nature, 291, 239–240), the mechanical causes underlying these costs and their changes with speed are not well understood. In particular, the paired, near‐simultaneous contacts of the trot is puzzling as it appears to demand a high mechanical work that could easily be avoided with distributed contacts, as with a “running walk” gait or “tolt.” Here, a simple condition is derived—a ratio including the pitch moment of inertia and back length—for which trotting is energetically advantageous because it avoids the energetic consequences of pitching. Pitching could also be avoided if the impulses from the legs were orientated through the center of mass. A range of idealized gaits is considered that achieve this zero‐pitch condition, and work minimization predicts a transition from trot to canter at intermediate speeds. This can be understood from the geometric principles of achieving a “pseudoelastic” collision with each impulse (Ruina et al., 2005, J Theoretical Biol, 14, 170‐192). However, at high speeds, a transition back to trot is predicted that is not observed in nature.