Ideal links are a class of bonds that satisfy the following condition: the total possible work of all reactions of these bonds on any possible displacements is zero.
Analytically formulated above condition of ideality for a system of material points can be formulated [1] as follows:
- ,
Where - the number of points included in the system, - resultant bond reactions applied to th point - possible movement of a given point (the round brackets denote the scalar product of vectors).
Examples of perfect connections:
1. Imposed on the material point connection in the form of a smooth surface (fixed or deformed over time), on which the point must move (here the possible displacements lie in the tangent plane to the given surface, and the coupling reaction of this plane is orthogonal, so the scalar product is zero ).
2. Internal relations in an absolutely solid body , ensuring the constancy of the distances between the current positions of the points of the body.
3. Contact of two absolutely solid bodies in contact with smooth surfaces when moving.
4. Contact of two absolutely solid bodies in contact when moving with absolutely rough surfaces.
See also
- Mechanical connection
- Principle of least coercion
- Axiom of connections
Notes
- ↑ Markeev, 1990 , p. 82
Literature
- Markeev A.P. Theoretical mechanics. - M .: Science, 1990. - 416 p. - ISBN 5-02-014016-3 .