Pseudomomentum: origins and consequences

The balance of pseudomomentum is discussed and applied to simple elasticity, ideal fluids, and the mechanics of inextensible rods and sheets. A general framework is presented in which the simultaneous variation of an action with respect to position, time, and material labels yields bulk balance laws and jump conditions for momentum, energy, and pseudomomentum. The example of simple elasticity of space-filling solids is treated at length. The pseudomomentum balance in ideal fluids is shown to imply conservation of vorticity, circulation, and helicity, and a mathematical similarity is noted between the evaluation of circulation along a material loop and the J-integral of fracture mechanics. Integration of the pseudomomentum balance, making use of a prescription for singular sources derived by analogy with the continuous form of the balance, directly provides the propulsive force driving passive reconfiguration or locomotion of confined, inhomogeneous elastic rods. The conserved angular momentum and pseudomomentum are identified in the classification of conical sheets with rotational inertia or bending energy.

讨论了假膜的平衡，并应用于简单的弹性，理想的流体以及不可延迟的杆和板的力学。提出了一个一般框架，其中在位置，时间和材料标签方面的作用同时变异产生了庞大的平衡法律和跳跃条件，以获得动量，能量和假膜体。简单的填充空间固体的弹性的示例是详细处理的。显示理想流体中的假体平衡表明涡度，循环和螺旋性的保存，并且在沿材料环的循环评估与断裂力学的J积分之间的数学相似性。伪小素平衡的整合，利用与平衡的连续形式得出的奇异源的处方，直接提供了推进力驱动被动的重新配置或限制性弹性杆的运动。在具有旋转惯性或弯曲能量的圆锥形板分类中鉴定出保守的角动量和假膜体。