Finite Rotations
نویسندگان
چکیده
We present an elementary discussion of two basic properties of angular displacements, namely, the anticommutation of finite rotations, and the commutation of infinitesimal rotations, and show how commutation is achieved as the angular displacements get smaller and smaller.
منابع مشابه
Objectivity of Incremental Constitutive Relations over Finite Time Steps in Computational Finite Deformation Analyses
Computational techniques, which preserve the objectivity of incremental constitutive relations, for finite elastic or inelastic materials, for finite time steps, during which the material elements may undergo finite rotations, are presented. These techniques are useful in finite deformation (finite rotations and finite strain) computational analysis of two as well as three dimensional solids an...
متن کاملEstimation of spinal loads using a detailed finite element model of the L4-L5 lumbar segment derived by medical imaging kinematics; a feasibility study
Introduction: Low back pain is the most prevalent orthopedic disorder and the first main cause of poor working functionality in developed as wells as many developing countries. In Absence of noninvasive in vivo measurement approaches, biomechanical models are used to estimate mechanical loads on human joints during physical activities. To estimate joint loads via musculoskelet...
متن کاملAn Historical Note on Finite Rotations
It is shown in this paper that Euler was first to derive the finite rotation formula which is often erroneously attributed to Rodrigues, while Rodrigues was responsible for the derivation of the composition formulae for successive finite rotations and the so-called Euler parameters of finite rotation. Therefore, based upon historical facts, the following nomenclature is suggested: Euler's finit...
متن کاملAn Efficient Strain Based Cylindrical Shell Finite Element
The need for compatibility between degrees of freedom of various elements is a major problem encountered in practice during the modeling of complex structures; the problem is generally solved by an additional rotational degree of freedom [1-3]. This present paper investigates possible improvements to the performances of strain based cylindrical shell finite element [4] by introducing an additio...
متن کاملDynamic Analysis of Finitely Stretched and Rotated Three-dimensional Space-curved Beams
The problem of transient dynamics of highly flexible three-dimensional space-curved beams, undergoing large rotations and stretches, is treated. The case of conservative force loading, which may also lead to configuration-dependent moments on the beam, is considered. Using the three parameters associated with a conformal rotation vector representation of finite rotations, a well-defined Hamilto...
متن کامل