On the rotational equations of motion in rigid body dynamics when using Euler parameters
نویسندگان
چکیده
Many models of three-dimensional rigid body dynamics employ Euler parameters as rotational coordinates. Since the four Euler parameters are not independent, one has to consider the quaternion constraint in the equations of motion. This is usually done by the Lagrange multiplier technique. In the present paper, various forms of the rotational equations of motion will be derived, and it will be shown that they can be transformed into each other. Special attention is hereby given to the value of the Lagrange multiplier and the complexity of terms representing the inertia forces. Particular attention is also paid to the rotational generalized external force vector, which is not unique when using Euler parameters as rotational coordinates.
منابع مشابه
Nonlinear Dynamics of the Rotational Slender Axially Moving String with Simply Supported Conditions
In this research, dynamic analysis of the rotational slender axially moving string is investigated. String assumed as Euler Bernoulli beam. The axial motion of the string, gyroscopic force and mass eccentricity were considered in the study. Equations of motion are derived using Hamilton’s principle, resulting in two partial differential equations for the transverse motions. The equations are ch...
متن کاملThe Transient Dynamics of a Beam Mounted on Spring Supports and Equipped with the Nonlinear Energy Sink
The transient dynamics of a beam mounted on springer-damper support and equipped with a nonlinear energy sink (NES) is investigated under the effects of shock loads. The equations of motion are derived using the Hamilton’s principle leading to four hybrid ordinary and partial differential equations and descritized using the Galerkin method. An adaptive Newmark method is employed for accurate an...
متن کاملLie Group Formulation of Articulated Rigid Body Dynamics
It has been usual in most old-style text books for dynamics to treat the formulas describing linear(or translational) and angular(or rotational) motion of a rigid body separately. For example, the famous Newton’s 2nd law, f = ma, for the translational motion of a rigid body has its partner, so-called the Euler’s equation which describes the rotational motion of the body. Separating translation ...
متن کاملHow to Draw Euler Angles and Utilize Euler Parameters
This article presents a way to draw Euler angles such that the proper operation and application becomes immediately clear. Furthermore, Euler parameters, which allow a singularity-free description of rotational motion, are discussed within the framework of quaternion algebra and are applied to the kinematics and dynamics of a rigid body. 1 Euler Angles In rigid body mechanics we need to keep tr...
متن کاملGeneralization of Rotational Mechanics and Application to Aerospace Systems
Generalization of Rotational Mechanics and Application to Aerospace Systems. (May 2005) Andrew James Sinclair, B.S., University of Florida; M.S., University of Florida Co–Chairs of Advisory Committee: Dr. John L. Junkins Dr. John E. Hurtado This dissertation addresses the generalization of rigid-body attitude kinematics, dynamics, and control to higher dimensions. A new result is developed that...
متن کامل