𝔖 Bobbio Scriptorium
✦   LIBER   ✦

The stability of a “sleeping” lagrange for with a vibrating suspension point

✍ Scribed by O.V. Kholostova

Publisher
Elsevier Science
Year
2000
Tongue
English
Weight
591 KB
Volume
64
Category
Article
ISSN
0021-8928

No coin nor oath required. For personal study only.

✦ Synopsis

The motion of a Lagrange top, the suspension point of which performs vertical harmonic oscillations of arbitrary frequency and amplitude, is considered. The particular motion where the top rotates about a vertically positioned axis of symmetry at a constant angular velocity (a "sleeping" top) is investigated. The complete solution of the problem concerning the stability of such motion for all permissible values of the parameters of the problem is given.

📜 SIMILAR VOLUMES

The stability of an inverted pendulum wi
The stability of an inverted pendulum with a vibrating suspension point
✍ A.A. Seyranian; A.P. Seyranian 📂 Article 📅 2006 🏛 Elsevier Science 🌐 English ⚖ 246 KB

The problem of stabilizing the upper vertical (inverted) position of a pendulum using vibration of the suspension point is considered. The periodic function describing the vibrations of the suspension point is assumed to be arbitrary but possessing small amplitudes, and slight viscous damping is tak

The dynamics of a spherical pendulum wit
The dynamics of a spherical pendulum with a vibrating suspension
✍ A.P. Markeyev 📂 Article 📅 1999 🏛 Elsevier Science 🌐 English ⚖ 436 KB

The motion of a spherical pendulum whose point of suspension performs high-frequency vertical harmonic oscillations of small amplitude is investigated. It is shown that two types of motion of the pendulum exist when it performs high-frequency oscillations close to conical motions, for which the pend

The equations of the approximate theory
The equations of the approximate theory of the motion of a rigid body with a vibrating suspension point
✍ A.P. Markeyev 📂 Article 📅 2011 🏛 Elsevier Science 🌐 English ⚖ 418 KB

The motion of a rigid body in a uniform gravity field is investigated. One of the points of the body (the suspension point) performs specified small-amplitude high-frequency periodic or conditionally periodic oscillations (vibrations). The geometry of the body mass is arbitrary. An approximate syste