Critical point of tori collision in quasiperiodically forced systems

Kuznetsov1, Neumann, Pikovsky

  • 1Institute of Radio-Engineering and Electronics of RAS, Saratov Division, Zelenaya 38, Saratov, Russia.

Related Concept Videos

First Law: Particles in Two-dimensional Equilibrium01:18

First Law: Particles in Two-dimensional Equilibrium

Recall that a particle in equilibrium is one for which the external forces are balanced. Static equilibrium involves objects at rest, and dynamic equilibrium involves objects in motion without acceleration; but it is important to remember that these conditions are relative. For instance, an object may be at rest when viewed from one frame of reference, but that same object would appear to be in motion when viewed by someone moving at a constant velocity.
Newton's first law tells us about the...
Coplanar Forces01:25

Coplanar Forces

Consider an object upon which multiple forces are acting. If the lines of action of each force lie within the same plane, the system can be considered coplanar. The Cartesian vector form can be used to resolve each force into its respective components. For a coplanar system, the system will be in equilibrium if each component of the resultant force equals zero and the resultant force on the system is zero. If the sum of the forces is not equal to zero, then the object will not be in equilibrium...
System of Forces and Couples01:16

System of Forces and Couples

In the analysis of structural systems, it is common to encounter members subjected to various forces and couple moments. Simplifying these systems can make the analysis more manageable and easier to understand. One approach to achieve this simplification is by moving a force to a point O that does not lie on its line of action and adding a couple with a moment equal to the moment of the force about point O.
The principle of transmissibility plays a crucial role in this process. According to...
Simplification of a Force and Couple System I01:18

Simplification of a Force and Couple System I

The concept of reducing a system of forces and couple moments to an equivalent system is essential in simplifying the analysis of rigid bodies. This reduction allows for more straightforward computation and understanding of the external effects produced by the system. In particular, systems with an equivalent resultant force and a resultant couple moment having perpendicular lines of action can be further reduced to a single equivalent resultant force acting along a new line of action. There...
Simplification of a Force and Couple System: II01:23

Simplification of a Force and Couple System: II

In a three-dimensional system, multiple forces can act on an object. These forces can be combined into a single equivalent force, known as the resultant force. Similarly, the moments generated by these forces can be combined into a single equivalent moment, the resultant couple moment. In certain situations, these two entities may not be mutually perpendicular, meaning they do not have a 90-degree angle between them. This unique condition requires a deeper understanding of the interplay between...
Equations of Equilibrium in Three Dimensions01:30

Equations of Equilibrium in Three Dimensions

When analyzing structures or systems at rest, it is necessary to ensure they are in equilibrium. This is where the vector and scalar equations of equilibrium come into play. These equations are crucial in ensuring a structure is stable and will not collapse or fall apart. The vector and scalar equations of equilibrium provide a framework for analyzing the forces acting on a body.
According to the vector equations of equilibrium, the vector sum of all the external forces acting on a body must...