Review study of using Euler angles and Euler parameters in multibody modeling of spatial holonomic and non-holonomic systems ( vol 10, pg 1707, 2022)

Modelling and simulation has become a general tool in product development of mechanical products. Building mathematical models of subsystems and components is one of the most important tasks in the analysis, design and optimization of any mechanical systems. Multibody system serves as a basis for many modern mathematical models of dynamic systems and has been applied in many areas of science. In the last decade, many algorithms and numerical manipulation tools have been developed to meet the increasing demands in the modeling and simulation of advanced mechanical systems in the industry. There are different methods used to define the body orientation in the spatial domain. Among these, Reference Point Coordinate Formulation with Euler Angles (RPCF-EA) and Reference Point Coordinate Formulation with Euler Parameters (RPCF-EP) are the most common ones. The main difference between them is that (RPCF-EA) defines the body orientation by using three successive angles, while (RPCF-EP) defines the same orientation using four parameters. In this paper, the formulation change of the equations of motion and the mapping of generalized forces into cartesian perspective are presented. In addition, three numerical examples are used to discuss the differences between using RPCF-EA and RPCF-EP in multibody systems with respect to the type of application. The first example demonstrates the suitability of each coordinates to model those systems subjected to a combination of holonomic and non-holonomic constraints. Second example, illustrates the differences between the two methods when modeling the types of joints that constraints the rotational motion, or make the relative rotation very small. Final example discusses the effectiveness of implementing RPCF-EA and RPCF-EP onto systems with gyroscopic motion, which has some numerical integration problems due to gimbal lock. © 2022, The Author(s), under exclusive licence to Springer-Verlag GmbH Germany, part of Springer Nature.