New Formulations on Acceleration Energies in Analytical Dynamics

Abstract

This paper presents new formulations on the higher order motion energies that are applied in the dynamic study of multibody mechanical systems in keeping with the researches of the main author. The analysis performed in this paper highlights the importance of motion energies of higher order in the study of dynamic behavior of fast moving mechanical systems, as well as in transient phase of motion. In these situations, are developed higher order time variations of the linear and angular accelerations. As a result, in the final part of this paper is presented an application that emphasizes this essential dynamic aspect regarding the higher order acceleration energies.

Advanced notions and differential principles of motion in analytical dynamics

“…Equation ( 7) is the mass matrix or inertia matrix of acceleration energies, refer to (8) with ( 9) it represents the column matrix of centrifugal and Coriolis terms, while refer to (10), it is named pseudo-inertial matrix of the acceleration energy. All three matrices are known, for example [1], [4]- [12].…”

“…Therefore, in this section the acceleration energy of second order is developed in explicit and matrix form. Starting from (1) and ( 2), the acceleration energy of second order becomes: According to [8]- [10], applying a few matrix and differential transformations, the explicit form of the acceleration energy of second order for a MBS is obtained as:…”

“…, representing the generalized accelerations of second order are also added. According to [8] - [10], following of the application a few of matrix and differential transformations, the matrix expression of the acceleration energy of second order is determined as follows:…”

“…According to [10] and [12], following of the application a few of matrix and differential transformations, the matrix expression of the acceleration energy of third order is defined as function of…”

“…The last two have the same matrix form with (24) and (26). All components of the above dynamics matrices are also determined with matrix exponentials described in the previous section, according to [10] and [12].…”