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该文亮点：

1. 因运动与力的定性、定量名义度量有助于更好地理解系统动力学，本文提出了一种新的基于连续介质的名义度量，用以表征振动与力；

2. 借助物质点法，新名义度量独立于推导动力学方程使用的列式方法和广义坐标；该新名义度量源于偏微分方程描述的连续介质力学平衡方程和Frenet几何标架；
   

3. 使用数据驱动科学（data-driven-science, DDS）方法定义了：一个具有名义曲率和扭转的名义连续空间曲线；一个包含所有合力（含惯性力）的名义瞬时运动平面（instantaneous motion plane, IMP）；以及一个合力沿其分量为零的名义瞬时零力轴（instantaneous zero-force axis, IZFA）;
   

4. 虽然使用物质点方法无需引入与姿态相关的转动方程，但IMP和IZFA的概念可用来定义会导致事故（如翻车的情况）的重要力矩分量的瞬轴。

Highlights:

1. Because qualitative and quantitative nominal measures of the kinematics and forces contribute to better understanding of the system dynamics, this paper proposes developing new continuum-based nominal measures for characterization of oscillations and forces.

2. By using a material-point approach, these new nominal measures, which have their roots in the continuum-mechanics partial-differential equations of equilibrium and Frenet geometry, are independent of the formulation or generalized coordinates used to develop the dynamic equations of motion. 
3. The paper uses a data-driven-science (DDS) approach to define a nominal continuum space-curve geometry with nominal curvature and torsion; a nominal instantaneous motion plane (IMP) which contains the resultant of all forces including the inertia forces; and a nominal instantaneous zero-force axis (IZFA) along which the resultant of all forces vanishes. 
4. While the use of the material-point approach eliminates the need for introducing moment equations associated with orientation coordinates, the IMP and IZFA concepts can be used to define the instantaneous axis of significant moment component, which can lead to accidents such as in the case of vehicle rollovers.

因缺乏对连续介质运动学和受力的准确名义度量，人们对复杂运动情况下固、液惯性力及其与重力势的耦合理解尚不深刻。名义度量的提出有助于更好理解系统动力学和稳定性，并明确系统故障和意外的根本原因。名义度量对制定危险品运输(transportation of hazardous materials, HAZMAT)操作和安全规范尤为重要。运输中液体的晃动对车辆动力学和稳定性的影响尚未被研究和理解透彻。固、液体有无限多自由度，具有分布式惯性和弹性，因此其动力学模型具有高维、非线性的特点。独立于模型阶数的运动学和受力的定性、定量低阶名义度量将有助于更好地理解系统动力学。

美国伊利诺伊大学芝加哥分校Ahmed A. Shabana教授在《国际机械系统动力学学报（英文）》（International Journal of Mechanical System Dynamics, IJMSD）发表“固体和液体名义几何与力的度量”研究简报。该文提出了一种新的基于连续介质的名义度量，用以表征振动与力；借助物质点法，新名义度量独立于推导动力学方程使用的列式方法和广义坐标；该新名义度量源于偏微分方程描述的连续介质力学平衡方程和Frenet几何标架。该文使用数据驱动（data-driven-science, DDS）方法定义了：一个具有名义曲率和扭转的名义连续空间曲线、一个包含所有合力（含惯性力）的名义瞬时运动平面（instantaneous motion plane, IMP），以及一个合力沿其分量为零的名义瞬时零力轴（instantaneous zero-force axis, IZFA）。连续介质的惯性力等于外界主动力、内应力和约束力之和，且各力的合力位于瞬时运动平面(IMP)内，IMP法向量定义了合力的主矩轴。平行于滚动轴的IMP法向量产生滚动力矩，平行于俯仰轴的IMP法向量产生俯仰力矩，而平行于偏航轴的IMP法向量产生偏航力矩。此外，IMP的方向决定了重力势对受力平衡的影响。使用DDS物质点法、用偏微分方程描述的连续介质力学平衡方程及有限元积分点的运动轨迹示踪(RMT)，可求解一个逆问题并用于定义名义惯性力体积分，确定连续介质名义切向和离心惯性力。对连续介质可定义其名义IMP和IZFA，进而确定参与力平衡定义的名义IMP超出量及其对重力的依赖。为分析运动轨迹而提出的物质点法独立于动力学方程的列式方法和广义坐标的选取。该文提出的名义度量对深入理解系统动力学和系统稳定性具有重要理论价值。

Abstract: Understanding solid- and fluid-inertia forces and their coupling with the gravity potential in complex motion scenarios is necessary for evaluating system stability and identifying root causes of system failure and accidents. Because solids and fluids have an infinite number of degrees of freedom and distributed inertia and elasticity, having meaningful qualitative and quantitative nominal measures of the kinematics and forces will contribute to a better understanding of the system dynamics. This paper proposes developing new continuum-based nominal measures for the characterization of the oscillations and forces. By using a material-point approach, these new nominal measures, which have their roots in the continuum-mechanics partial-differential equations of equilibrium and Frenet geometry, are independent of the formulation or generalized coordinates used to develop the dynamic equations of motion. The paper proposes a data-driven-science approach to define a nominal continuum space-curve geometry with nominal curvature and torsion; a nominal instantaneous motion plane (IMP), which contains the resultant of all forces including the inertia forces; and a nominal instantaneous zero-force axis (IZFA) along which the resultant of all forces vanishes. While using the material-point approach eliminates the need for introducing moment equations associated with orientation coordinates, the IMP and IZFA concepts can be used to define the instantaneous axis of significant moment components, which can lead to accidents such as in the case of vehicle rollovers.