基于刚体平面运动微分方程的达朗贝尔原理推导

Deduction of D’Alembert’s principle based on the plane motion differential equation of rigid body

给出了达朗贝尔原理新的推证方法,得出了适用于三种运动形式(平行移动、定轴转动和平面运动)刚体惯性力及惯性力偶的统一添加模式:惯性力和惯性力偶都在质心处,惯性力大小等于刚体质量与质心加速度的乘积,并与质心加速度方向相反;惯性力偶大小等于刚体对质心轴的转动惯量乘以角加速度,并与角加速度方向相反。

This paper gives a new deduction of D’Alembert’s principle.A unified addition mode of rigid body inertial force and inertial couple suitable for three movement forms(translation,fixed axis rotation and plane motion)is obtained.Both inertial force and inertial couple are at the center of mass.The magnitude of inertial force is equal to the product of rigid body mass and centroid acceleration.The inertial force direction is opposite to the centroid acceleration.The magnitude of inertial couple is equal to the product of inertial moment to the centroid axis and the angular acceleration.The inertial couple direction is opposite to the angular acceleration.