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Applications and case studies
Published in Roderic S. Lakes, Viscoelastic Solids, 2017
Viscoelastic elastomers are also used in the form of inertial dampers to reduce settling time during rapid angular accelerations of head-positioning motors in computer disk drives [10.2.1], and to reduce resonant vibration in high-speed robots. Nutation motion of spinning rotors mounted upon gimbals (pivot joints) occurs when a perturbing torque is suddenly applied. Nutation is an oscillatory motion of the spin axis. In some gyroscopic, aerospace, and satellite applications it is desirable to damp this nutation motion. Such damping may be achieved by attaching masses to the rotor by a compliant, viscoelastic stalk or annulus [10.6.7, 10.6.8]. The nutation motion causes an oscillatory strain in the viscoelastic material, dissipating energy and damping the motion.
The Earth–Sun Relationship
Published in Matt Fajkus, Dason Whitsett, Architectural Science and the Sun, 2018
Within the long cycle of precession, the Earth also rocks slightly on its axis over a period of 18.6 years, slightly changing the obliquity of the ecliptic. This phenomenon, known as nutation, is the result of the gravitation pull of the moon on the Earth along its orbital path, which is inclined approximately 5° relative to the ecliptic plane. For design purposes, precession and nutation are not significant factors and may be ignored.
Multibody system design based on reference dynamic characteristics: gyroscopic system paradigm
Published in Mechanics Based Design of Structures and Machines, 2023
Ayman A. Nada, Abdullatif H. Bishiri
On the other hand, the study of the gyroscopic motion is one of the most interesting problems in spatial dynamics (Lawrence 1998; Ng 2005; Butikov 2006). This problem occurs when the orientation of the axis of rotation of a rotating body change during the movement, this body resists changes in orientation with no external inputs (Shabana et al. 2011). A mechanical gyroscope shows a number of physical phenomena, including precession and nutation and implemented in many industrial applications (Passaro et al. 2017). In some applications, designers have to present methods of balancing its impact, while in others, it can be used to modify the mechanism’s performance. In these two cases, the Gyrotorque action induces a finite precessional momentum gain in each angular direction of the oscillation. This precessional momentum gain in one direction of oscillation is limited with respect to change of its coordinates (Usubamatov 2016; Kellogg 1965).
The angular characteristics of Moon-based Earth observations
Published in International Journal of Digital Earth, 2020
Huadong Guo, Yuanzhen Ren, Guang Liu, Hanlin Ye
The Earth’s orientation is defined as the rotation from the Earth’s crust (the terrestrial system) to a geocentric set of axes tied to quasars (a geocentric celestial system, distinguished from the reference celestial system, which has its origin in the barycenter of the solar system). More specifically, it means the rotation between a rotating geocentric set of axes linked to the Earth Gxyz (the terrestrial system determined by the coordinates of observing stations) and a non-rotating geocentric set of axes linked to inertial space GXYZ (the celestial system determined by the coordinates of stars, quasars, and objects in the solar system). The common method of describing the rotation between these two systems is to specify the rotation matrix. Rotation is split into three components; the precession-nutation of the figure axis in space, the diurnal rotation around the celestial intermediate pole (Capitaine et al. 2003), and the polar motion of the celestial intermediate pole with respect to the terrestrial crust. The Earth’s orientation is then obtained by inserting these parameters in the coordinate transformation between the Celestial Reference Frame and the Terrestrial Reference Frame.
Modelling and analysis of a gyrostat elastically attached to a vehicle
Published in Vehicle System Dynamics, 2018
Andreas Zwölfer, Günter Bischof
The imaginary parts of the eigenvalues represent the natural angular frequencies of the system, which are associated with one cylindrical and two conical modes. The low-frequency conical mode represents the gyrostat's nutation, the high-frequency mode its precession. The nutation frequency increases with the rotor frequency, the precession frequency , on the other hand, decreases. The frequency of cylindrical modes , which represent the pendulous motion of the gyrostat, is independent of the gyrostat's spin. The three different natural frequencies , and of the gyrostat defined by the parameters in Table 2 are listed in Table 3 for a series of bearing stiffnesses .