DOI: https://doi.org/10.31319/2519-8106.2(39)2018.154209

MATHEMATICAL MODELING OF GYROSCOPE DYNAMICS BASED ON QUATERNION

Кирило Сергійович Красніков

Анотація


The paper is devoted to the mathematical description of gyroscope dynamics using quaternion as nonsingular representation of rotation. In the previous works related to wire dynamics the angles of spherical coordinate system can give wrong results in common configurations of a wire injected into a melt. Present paper considers two models that are constructed using Euler-Lagrange equations and compared in the problematic situation when one model gives unexpected trajectory of motion. Also for checking the model another experiment with precession was carried out. Presented pictures show 3d-model of gyroscope precessing under force of gravity with different speeds.

Ключові слова


gyroscope; Euler-Lagrange equations; quaterion

Повний текст:

PDF (English)

Посилання


Haug Edward J. Computer aided kinematics and dynamics of mechanical systems. Volume I: Basic methods. – Massachusetts: Allyn and Bacon, Inc, 1989. – 500 p. ISBN:0-205-11669-8.

Baumgarte, J. Stabilization of constraints and integrals of motion / Computer methods in applied mechanics and engineering, Vol. 1, 1972. – pp. 1–16.

Бранец В.Н. Применение кватернионов в задачах ориентации твердого тела. / В.Н. Бранец, И.П. Шмыглевский. – М: «Наука», 1973. – 320 с.

Погорелов Д.Ю. Введение в моделирование динамики систем тел: уч. пособие. / Д.Ю. Погорелов. – Брянск: БСТУ, 1997. – 153 с. ISBN 5-230-02435-6

Модель прецесії гіроскопа [Електронний ресурс] // Youtube-канал “Kireal Lab”. Режим доступу: https://youtu.be/0K3n3TelCjg (дата звернення 10.09.2018 р.)