# Integrating rotation and angular velocity from curvature
ID Saje, Miran (Avtor), ID Ogrin, Anita (Avtor) URL - Predstavitvena datoteka, za dostop obiščite http://dx.doi.org/10.1016/j.advengsoft.2015.02.010 Izvleček
The problem of integrating the rotational vector from a given angular velocity vector is met in such diverse fields as the navigation, robotics, computer graphics, optical tracking and non-linear dynamics of flexible beams. For example, if the numerical formulation of non-linear dynamics of flexible beams is based on the interpolation of curvature, one needs to derive the rotation from the assumed curvature field. The relation between the angular velocity and the rotation is described by the first-order quasilinear differential equation. If the rotation is given, the related angular velocity is obtained by the differentiation. By contrast, if the angular velocity is given, the related rotations are obtained by the integration. The exact closed-form solution for the rotation is only possible if the angular velocity is constant in time. In dynamics of non-linear flexible spatial beams, the problem of integrating rotations from a given angular velocity becomes even more complex because both the angular velocity and the curvature need simultaneously be integrated and are both functions of space and time. As the angular velocity and the curvature are assumed to be analytic functions, they must satisfy certain integrability conditions to assure the unique rotation is obtained from the two differential equations. The objective of the present paper is to derive approximate, yet closed-form solutions of the following problem: for a given curvature vector, determine both the rotation and the angular velocity. In order to avoid the singularity of kinematic relations, the quaternions are used for the parametrization of rotations, and the integrations are partly performed in the four-dimensional quaternion space. The resulting closed-form expressions for the rotational and angular velocity quaternions are ready to be used in the finite-element formulations of the dynamics of flexible spatial beams as interpolating functions. The present novel solution is assessed by comparisons of the numerical results with analytical solutions for variety of oscillating curvature functions, as well as with the solutions of the quaternion-based midpoint integrator and the Runge-Kutta-based Crouch-Grossman geometrical methods CG3 and CG4. 2015 The Authors. Published by Elsevier Ltd. This is an open access article under the CC BY-NC-NDlicense

Jezik: Angleški jezik curvature, angular velocity, rotational quaternion, integration of rotational quaternion from curvature, integration of angular velocity from curvature, initial-value problem Delo ni kategorizirano (r6) 1.01 - Izvirni znanstveni članek FGG - Fakulteta za gradbeništvo in geodezijo 2015 Str. 26-42 Letn. 85 20.500.12556/RUL-83393 531 0965-9978 10.1016/j.advengsoft.2015.02.010 7017313 14.06.2016 1220 342     AddThis uporablja piškotke, za katere potrebujemo vaše privoljenje.Uredi privoljenje...

## Gradivo je del revije

Naslov: Advances in engineering software Adv. eng. softw. Elsevier Applied Science 0965-9978 34540032 ## Sekundarni jezik

Jezik: Neznan jezik ukrivljenost, kotna hitrost, rotacijski kvaternion, integracija rotacijskega kvaternion iz ukrivljenosti, integracija kotne hitrosti iz ukrivljenost i, problem začetno vrednosti

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