M3 Impulsive Locomotion

Topic

Impulsive locomotion generates a mechanical impulse concentrated within a very short time interval to displace the center of mass—either vertically, as in jumping, or horizontally, as in certain forms of bounding movement.

Before generating this impulse, many jumpers perform a countermovement cycle: the body first descends, eccentrically preloading the tendons—that is, stretching them while the muscle contracts to brake the descent. This preload stores additional elastic energy that supplements the energy generated by the muscle during concentric contraction at takeoff, thereby boosting the peak power the animal achieves just before leaving the ground. In the red kangaroo, the efficiency of repeated jumping increases with travel speed, precisely because at higher speeds, a larger fraction of the total energy is recovered elastically rather than having to be actively generated by the muscle.

Once the animal takes off, its center of mass follows a ballistic trajectory during the jump's aerial phase, subject only to gravity; in a vacuum—absent air resistance—the horizontal distance achieved is maximized when the takeoff angle is forty-five degrees relative to the ground.

This ballistic trajectory concludes upon landing, where the body must absorb an impact force that can reach five to twenty times the animal's body weight. This force is dissipated through eccentric muscle work distributed across the ankle, knee, and hip, with each joint absorbing a portion of the impact energy rather than allowing it to concentrate on a single structure. In certain specialized jumpers, such as the bushbaby or the frog, the takeoff power per unit of muscle mass exceeds the maximum power that the isolated muscle itself can generate through contraction alone. This is possible because the muscle does not release all that power directly; instead, it first loads a tendon with elastic energy during a slower phase, and the tendon subsequently releases that energy in a sudden burst—far more rapidly than the muscle could contract on its own—acting like a catapult that instantly discharges the previously stored elastic energy.

The repetitive jumps characteristic of "hopping"—mentioned earlier as a form of this impulsive locomotion—are periodic and recur in a self-similar pattern from one jump to the next. The entire system oscillates at its own resonant frequency, which is the frequency requiring the least active energy to sustain the hopping motion. In kangaroos, the animal's naturally preferred hopping frequency aligns precisely with the resonant frequency of the spring-mass system formed by the elastic tendons in their hind limbs.

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