ON THE n-ORDER ACCELERATIONS DISTRIBUTION DURING RIGID MOTION (original) (raw)

Higher-Order Kinematics of Rigid Bodies. A Tensors Algebra Approach

Kecskeméthy A., Geu Flores F., Carrera E., Elias D. (eds) Interdisciplinary Applications of Kinematics. Mechanisms and Machine Science, vol 71. Springer, Cham, 2019

The problem of determining the tensors and the vector invariants that describe the vector field of the nth order accelerations is generally avoided in rigid body kinematics. This paper extends the discussion from velocities and accelerations to nth order accelerations. Using the tensor calculus and the dual numbers algebra, a computing method for studying the nth order acceleration field properties is proposed for the case of the general motion of the rigid body. This approach uses the isomorphism between the Lie group of the rigid displacements SE 3 and the Lie group of the orthogonal dual tensors SO 3. 20.1 Velocity and Acceleration Fields in Rigid Body Motion The general framework of this paper is a rigid body that moves with respect to a fixed reference frame 0. Consider another reference frame {} originated at a point Q that moves together with the rigid body. Let ρ Q denote the position vector of point Q with respect to the frame 0 , v Q its absolute velocity and a Q its absolute acceleration. The vector parametric equation of motion is: ρ = ρ Q + Rr, (20.1) where ρ represents the absolute position of a generic point P of the rigid body with respect to 0 and R = R(t) is an orthogonal proper tensorial function in SO R 3 [2, 5]. Vector r is constant and it represents the relative position vector of the arbitrary point P with respect to {}. The results of this section succinctly present the velocity and acceleration vector field in rigid body motion. These results lead to the generalization presented in the next section.