Mathematical Methods of Classical Mechanics pp 98-122 | Cite as

# Oscillations

Chapter

## Abstract

Because linear equations are easy to solve and study, the theory of linear oscillations is the most highly developed area of mechanics. In many nonlinear problems, linearization produces a satisfactory approximate solution. Even when this is not the case, the study of the linear part of a problem is often a first step, to be followed by the study of the relation between motions in a nonlinear system and in its linear model.

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### References

- 41.If the equilibrium position is unstable, we will talk about “unstable small oscillations” even though these motions may not have an oscillatory character.Google Scholar
- 42.If one wants to, one can introduce a euclidean structure by taking the first form as the scalar product, and then reducing the second form to the principal axes by a transformation which is orthogonal with respect to this euclidean structure.Google Scholar
- 43.
- 45.The distance between two linear systems with periodic coefficients, (math), is defined as the maximum over
*t*of the distance between the operators*B*_{1}(*t*) and*B*_{2}(*t*).Google Scholar - 46.
- 47.Cf., for example, the problem analyzed below.Google Scholar

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