title: ÐÑÑÐ»ÐµÐ´Ð¾Ð²Ð°Ð½Ð¸Ðµ ÑÐµÐ¶Ð¸Ð¼Ð¾Ð² ÑÐ¿ÑÐ°Ð²Ð»ÑÐµÐ¼Ð¾Ð³Ð¾ Ð´Ð²Ð¸Ð¶ÐµÐ½Ð¸Ñ Ð³Ð¸ÑÐ¾ÑÐºÐ¾Ð¿Ð¸ÑÐµÑÐºÐ¾Ð³Ð¾ Ð¼Ð°ÑÑÐ½Ð¸ÐºÐ° Ð² ÐºÐ°ÑÐ´Ð°Ð½Ð¾Ð²Ð¾Ð¼ Ð¿Ð¾Ð´Ð²ÐµÑÐµ
title: Ð²ÑÐ¿ÑÑÐºÐ½Ð°Ñ ÐºÐ²Ð°Ð»Ð¸ÑÐ¸ÐºÐ°ÑÐ¸Ð¾Ð½Ð½Ð°Ñ ÑÐ°Ð±Ð¾ÑÐ° Ð±Ð°ÐºÐ°Ð»Ð°Ð²ÑÐ°
titleType: Subtitle
title: Study of controlled movement modes of a gyroscopic pendulum fixed in a gimbal suspension
Creators: name: Ð¡Ð°ÑÐ²Ð¸Ð»Ð¾Ð², ÐÐ¾Ð½ÑÑÐ°Ð½ÑÐ¸Ð½
Publisher: name: Ð¡Ð°Ð½ÐºÑ-ÐÐµÑÐµÑÐ±ÑÑÐ³ÑÐºÐ¸Ð¹ Ð¿Ð¾Ð»Ð¸ÑÐµÑÐ½Ð¸ÑÐµÑÐºÐ¸Ð¹ ÑÐ½Ð¸Ð²ÐµÑÑÐ¸ÑÐµÑ ÐÐµÑÑÐ° ÐÐµÐ»Ð¸ÐºÐ¾Ð³Ð¾
Year: 2023
Subjects: Ð³Ð¸ÑÐ¾ÑÐºÐ¾Ð¿Ð¸ÑÐµÑÐºÐ¸Ð¹ Ð¼Ð°ÑÑÐ½Ð¸Ðº
ÐºÐ°ÑÐ´Ð°Ð½Ð¾Ð² Ð¿Ð¾Ð´Ð²ÐµÑ
ÐºÐ°ÑÐ´Ð°Ð½Ð¾Ð²Ñ ÑÐ³Ð»Ñ
ÑÐ¸Ð·Ð¸ÑÐµÑÐºÐ¸Ðµ Ð¿ÑÐ¸Ð½ÑÐ¸Ð¿Ñ
ÑÐ¿ÑÐ°Ð²Ð»ÑÑÑÐ¸Ðµ Ð¼Ð¾Ð¼ÐµÐ½ÑÑ
gyroscopic pendulum
gimbal suspension
gimbal angles
physical principles
control moments

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description: The paper discusses the issues of controlling the movement of a gyroscopic pendulum fixed in a gimbal suspension and having three degrees of freedom. To form the control moments in the suspension joints, it is proposed to use physical analogies and correlate the action of these moments with the dissipative forces of external viscous friction, friction in the gimbal joints and internal friction, as well as with the forces of inertia and gyroscopic forces. Six modes of controlled movement of the system are considered, which allow achieving various final goals. It is shown that it is possible to completely suppress the movements of a gyroscopic pendulum, transfer it to the mode of oscillation of a spherical or physical pendulum, bring it to the mode of rotation around a fixed vertical axis, enter the mode of regular precession, and also strengthen or weaken the gyroscopic structure of the equations of motion. The discussion of these modes of controlled motion of a gyroscopic pendulum is accompanied by the construction of equations of motion both within the framework of the original nonlinear model and for simplified linear or weakly nonlinear models. In addition, numerical integration of the equations of controlled motion of a gyroscopic pendulum is carried out in the MATLAB package and graphical dependencies are constructed illustrating the control processes. The results obtained are theoretically interesting and may be useful for specific practical applications in the field of gyroscopic technology.