The Splitting of Separatrices, the Branching of Solutions, and Nonintegrability of Many-Dimensional Systems. Application to the Problem of the Motion of a Spherical Pendulum with an Oscillating Suspension Point

2016 ◽  
Vol 214 (6) ◽  
pp. 755-801
Author(s):  
S. A. Dovbysh
Keyword(s):  
Spherical Pendulum ◽  
Suspension Point ◽  
Branching Of Solutions ◽  
Splitting Of Separatrices

scholarly journals Areas of attraction of the pendulum under the influence of oblique vibration of the suspension point

2021 ◽  
Vol 8 (3) ◽  
pp. 511-522
Author(s):  
Аlexander G. Petrov ◽  
Keyword(s):  
Inverse Problem ◽  
High Frequency ◽  
Velocity Vector ◽  
Vibration Characteristics ◽  
Vibration Velocity ◽  
Spherical Pendulum ◽  
Suspension Point ◽  
High Frequency Vibration ◽  
Stable Position ◽  
Regions Of Attraction

The inverse problem of stabilizing a spherical pendulum in a given position by means of high-frequency vibration of the suspension point is posed. The position of the pendulum is determined by the angle between the pendulum rod and the vertical. For any given position of the pendulum, a one-parameter series of oblique vibration characteristics (the amplitude of the vibration velocity and the angle between the vibration velocity vector and the vertical) is found to stabilize the pendulum in this position. For the obtained series, the regions of attraction are determined (the initial points from which a given stable position of the pendulum will be established under the influence of vibration).

Spherical pendulum as an analogy to Kepler’s second law

2019 ◽  
Vol 55 (1) ◽  
pp. 015002
Author(s):  
T A Canassa ◽  
W P S Freitas ◽  
J V B Ferreira ◽  
A M B Goncalves
Keyword(s):  
Second Law ◽  
Spherical Pendulum

Simulation of oscillatory processes in the MVSTUDIUM package

2022 ◽  
Vol 14 (4) ◽  
pp. 139-148
Author(s):  
Aleksandr Poluektov ◽  
Konstantin Zolnikov ◽  
V. Antsiferova
Keyword(s):  
Mathematical Model ◽  
Friction Force ◽  
Computer Models ◽  
3D Models ◽  
Oscillatory Process ◽  
Suspension Point ◽  
Factors Affecting ◽  
2D And 3D ◽  
The Mathematical Model ◽  
Oscillatory Processes

The mathematical model and algorithms of oscillatory movements are considered. Various factors affecting the oscillatory process are considered. Oscillatory movements are constructed in the MVSTUDIUM modeling environment. The schemes of three computer models demonstrating oscillatory processes are determined: a model of a pendulum with a non-movable suspension point, a model of a pushing pendulum with friction force and a model of a breaking pendulum. Classes are being built to execute models with embedded properties, as well as with the ability to export the created classes to other models, and embed classes created by the program developer into the model. Creation of 2D and 3D models of oscillatory processes, an experiment behavior map and a virtual stand.

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