INM-Leibniz Institute for New Materials and Saarland University, Campus D2 2, D-66123 Saarbrücken, Germany.
J Theor Biol. 2012 Mar 21;297:17-25. doi: 10.1016/j.jtbi.2011.12.003. Epub 2011 Dec 9.
We analyze theoretically the moment of inertia of the desert ant Cataglyphis (C. bicolor and C. fortis) around a vertical axis through its own center of mass when the animal raises its gaster to a vertical position. Compared to the value when the gaster is horizontal, the moment of inertia is reduced to one half; this implies that when increasing its angular acceleration the ant need apply only half the level of torque when the gaster is raised, compared to when the gaster is lowered. As an example, we analyze the cases of an ant running on circular and sinusoidal paths. In both cases, the ant must apply a sideways thrust, anti-roll and anti-pitch torques to avoid toppling, and, on the circular path when accelerating and throughout the sinusoidal trajectory, a torque to enable turning as the path curves. When the ant is accelerating in a very tight circle or running on a very narrow sinusoidal path, in which the amplitude of the sinusoid is less than the length of the ant's body, the forces required for the turning torque can equal and exceed those required for the sideways thrust, and can be reduced significantly by the ant raising the gaster, whereas the foot-thrust for the anti-roll and anti-pitch torques rises only modestly when the gaster is up. This suggests that there may be an evolutionary advantage for employing the gaster-raising mode of locomotion, since this habit will allow desert ants to use lower forces and less energy, and perhaps run faster on more tortuous paths.
我们从理论上分析了沙漠蚂蚁(双色弓背蚁和强壮弓背蚁)在将腹部抬至垂直位置时绕自身质心垂直轴的转动惯量。与腹部水平时相比,转动惯量减小到一半;这意味着当蚂蚁增加角加速度时,与腹部下降相比,蚂蚁在抬起腹部时只需要施加一半的力矩。作为一个例子,我们分析了蚂蚁在圆形和正弦形路径上奔跑的情况。在这两种情况下,蚂蚁都必须施加横向推力、防滚和防俯仰力矩,以避免翻倒,并且在圆形路径上加速和整个正弦轨迹中,为了使路径转弯,还需要施加一个扭矩。当蚂蚁在非常紧的圆形或在非常狭窄的正弦形路径上加速时,其中正弦波的幅度小于蚂蚁身体的长度,用于转向扭矩的力可以等于甚至超过用于横向推力的力,并且可以通过蚂蚁抬起腹部而显著降低,而用于防滚和防俯仰力矩的脚推力仅当腹部抬起时适度增加。这表明,采用腹部抬起的运动模式可能具有进化优势,因为这种习惯将允许沙漠蚂蚁以较低的力和较少的能量运动,并且可能在更曲折的路径上跑得更快。